First there are an infinite number of jivas; infinite means infinite. Second, also remember that all jivas may not be alive at this instant; there are jivas that are going through a period of death now also. Third, an individual jiva takes birth that is necessary for its karma at that given point; so once having died, a new birth may be a hundreds or a thousands years after its last birth. Fourth, remember that you, yourself, the 'I" that you think of as yourself, is not the only jiva inside your body. Each individual cell that compose your body as well as the hundreds of millions of bacteria in you, has its own separate jiva which is going through its own evolution. Infinite means infinite.
When we speak of jiva, we are talking about the atman embodied. You refer to the jiva as being an aspect of the subtle body. This is not the meaning of jiva. Jiva means the embodied atman. The subtle body consists of 3 kosas. So the atman when embodied in either the subtle or gross body is jiva. The individual atman is the same as the Atman which is the same as Brahman. Individual jivas are the reflection of Brahman.
In his Introduction (sub-heading The Jiva's real nature) to his translation of the Brahma Sutras, Swami Vireswarananda says (pp xxix-xxxi, also available here - http://www.wisdomlib.org/hinduism/book/brahma-sutras/d/doc62756.html):
Now we come to Sutras 2. 3. 16-53 which deal with the nature of the soul and its relation to Brahman. All except Sankara interpret these Sutras to mean that the soul is atomic, an agent, and a part of the Lord. Sankara alone says that the atomicity, agency, and being a part are not the Jiva’s real nature, but its nature as a Samsârin (transmigrating entity) and that in reality it is all-pervasive and identical with Brahman.
The author defines Brahman as the cause etc. of this world of sentient and insentient things in Sutra 2, referring to the Taittiriya text, “That out of which all these creatures are born" etc. (3. 1). It is clear, therefore, that the world of sentient and insentient things has sprung from Brahman. Hence the Jivas too have sprung from the Lord. But in Sutra 17 the author says that the individual soul is not produced. Thus he contradicts his definition and also the enunciation of the scriptures that “by the knowledge of one thing everything else is known” (Chh. 6. 1). The Sutrakâra at every place makes this enunciation the corner-stone of his argument. So we have to reconcile it and the author’s definition of Brahman with his statement in Sutra 17 which drives us to the conclusion that the Jiva as such, as a Samsârin, is an effect, but in its real nature it is eternal and identical with Brahman. That the nature of the Jiva as we experience it is unreal is made clear by him in Sutra 16. What originates is its connection with its adjuncts, gross and subtle, which is unreal. From this standpoint it is also clear why the author treats the question of the Jiva’s nature and its relation to Brahman in this section which reconciles contradictions in the Sruti texts with respect to creation. There are different statements about the nature of the Jiva also and these he reconciles in this section, showing thereby that in its real nature it is not created and is identical with Brahman, but as a Samsârin it is an effect, atomic, an agent, and a part of Brahman.
Even as Iswara or Brahman limited by Nescience is not eternal, so is the Jiva limited by the body, mind, etc, not eternal, but in its true nature it is eternal. Bereft of their Upâdhis both are Pure Intelligence and identical. That is why the Taittiriya Upanishad after saying, “Existence, Knowledge, Infinite is Brahman” (2. 1) says, “From That verily—from this Self—is the ether born” etc. (2. I), thus identifying the self as bereft of all its Upâdhis with Brahman. Taittiriya 2. 1, and 3. 1 cited by the Sutrakâra in his definition of Brahman all refer to the same Pure Intelligence. Thus the one ‘Existence, Knowledge, Infinite’ which is Pure Intelligence, reflected in Nescience is Iswara, and reflected in the Antah-karana (internal organ) is the Jiva, which is borne out by the scriptural statement, “This Jiva has the effect for the adjunct and Īswara has the cause for the adjunct” (Sukharahasya Up. 2. 12). This seems to be the true view-point which has guided the aphorist in framing the Sutras of Section 3, Chapter II and in which sense Sankara also has interpreted them. The enunciation also is not contradicted according to this interpretation.
According to Râmânuja the souls are really effects of Brahman but have existed in It from all eternity as a mode or Prakâra of Brahman. So also have the elements. Yet the latter are said to originate, as at the time of creation they undergo an essential change of nature. But the souls do not undergo such a change, they are always cognizing agents, but at the time of creation there is an expansion of thêir intelligence and in this sense alone, i.e. in the sense that there is no essential change in their nature at creation, are the souls said to be not created (vide Sri Bhâshya 2. 3. 18) while the elements which undergo change in their essential nature are said to be created. Bâdarâyana nowhere says that the souls and Prakriti which form the body of Brahman are Its effects; nor does he anywhere declare such a difference between the souls and the elements. Again, according to Râmânuja Brahman means not pure Being but as qualified by the souls and matter for Its body. This very conception of Brahman establish that the relation between the souls and Brahman is as between a quality and the thing qualified and consequently 2. 3. 43 is redundant if the word ‘part’ there should be interpreted to convey this idea.
Râmânuja sees a refutation of Advaita in Sutras 50-53. This does not seem to be intelligible at all, for the Advaitins do not say that the Jiva is all-pervading in its relative state. It is so in the state of release. Sankara makes it clear that the Jiva as such is limited and subject to injunctions and prohibitions, through its connection with a gross body (2. 3. 48), and that even after the gross body falls, on account of its finer Upâdhis, the Antahkarana etc. which accompany it even after death (4. 2. 1-0), it still continues to be individualized (2. 3. 30), and so there is no confusion in fruits of actions done in the gross body (2. 3. 49 and 50). It is only when this Upâdhi also, which being something created and not eternal (vide 2. 4) and therefore liable to destruction, is rent asundei, that the Jiva attains its real nature and is all-pervading. As such. Râmâjiuja’s refutation of Advaita falls flat. Sankara’s interpretation of these Sutras on the other hand is happy. The Sutrakâra, having established that the Jiva in its relative state is atomic and an agent but in reality aH-pervading, refutes the view of those who hold that the Jivas are many and all-pervading in their relative state itself. Nimbârka and Vallabha also see the same subject in this topic which shows that Râmânuja’s attempt to refute Advaita is far-fetched and not at all what the Sutrakâra (aphorist) means.
Nimbârka too regards the Jivas and Prakriti as effects of Brahman; but while matter undergoes further modification after creation, the souls do not and in this sense the soul is said to be eternal by him also. Such a view stands refuted by the same arguments as are applied against Râmânuja’s view. Coming to Sutra 43 which says the Jiva is different as well as non-different from Brahman, it has already been shown by Sankara in 2. 1. 14 that such a thing is not possible in the same entity and that nondifference alone is real.
Let us now conclude this topic by considering the reasonableness or otherwise of taking Sutras 19-28 as the decisive view of the author. According to this view the soul is atomic, for the Sruti declares it to be so (Mu. 3. 1. 9) and other texts mention its passing out of the body, going to heaven, etc. But then the Sruti also describes the Supreme Self as atomic in texts like, “Smaller than a grain of rice, smaller than a grain of barley” etc. (Chh. 3. 14. 3). So how can we say that the Jiva alone is atomic and not the Lord? It may be said that texts say that Brahman is all-pervading. “All-pervading like the ether and eternal” etc.; “Greater than the sky, greater than heaven” etc. But then the Sruti texts describe the soul also as all-pervading: “He is indeed the great unborn Self” (Brih. 4. 4. 22); “Just as when a pot is carried, the pot alone is carried, not the ether inside it, even so is the Jiva compared to the ether,” which expressly says it is all-pervading. Nor will it serve any purpose to say that Brahman, being the material cause of the world, must be all-pervasive, for even the atomic Jiva creates several bodies (Kâyavyuha) and rules them and so Brahman though the material cause can yet be atomic. So neither by the Sruti texts nor by reasoning can the differentiation of Brahman and the Jiva as all-pervasive and atomic be justified. But according to Advaita there is no disparity in its reasoning in the two cases. Brahman due to Upâdhi (adjunct) appears atomic but in reality It is all-pervasive. So also is the Jiva in its real nature all-pervading and therefore identical with Brahman, though it appears to be atomic, an agent and so on owing to its limiting adjunct, the Antahkarana. The primary texts say that Brahman and the Jiva in its real nature are all-pervading. The texts which speak of atomicity etc. are of a secondary import and so have to be explained otherwise.
You also refer to Saguna Brahman coming into contact with Prakriti. Saguna Brahman is Brahman (Nirguna) seen through Maya or the gunas. You cannot think of Sanguna Brahman separate from Prakriti. Krishna says in Gita 9.7 (Swami Gambhirananda translator):
O son of Kunti, all the beings go back at the end of a cycle to My Prakriti. I project them forth again at the beginning of a cycle.
and Sankara's commentary on this verse says:
...to My Prakrti which consists of the three gunas (qualities; see 7.13) and is (called My) lower Nature...
Finally, Swami Vivekananda says (Complete Works, V7, pp 191-193 and here under the heading Conversations and Dialogues, sub-heading From The Diary of a Disciple sub-sub-heading XV):
Disciple: Sir, is there any such statement in the Upanishads that Ishvara is an all-powerful Person? But people generally believe in such an Ishvara.
Swamiji: The highest principle, the Lord of all, cannot be a Person. The Jiva is an individual and the sum total of all Jivas is the Ishvara. In the Jiva, Avidyâ, or nescience, is predominant, but Ishvara controls Maya composed of Avidya and Vidyâ and independently projects this world of moving and immovable things out of Himself. But Brahman transcends both the individual and collective aspects, the Jiva and Ishvara. In Brahman there is no part. It is for the sake of easy comprehension that parts have been imagined in It. That part of Brahman in which there is the superimposition of creation, maintenance and dissolution of the universe has been spoken of as Ishvara in the scriptures, while the other unchangeable portion, with reference to which there is no thought of duality, is indicated as Brahman. But do not on that account think that Brahman is a distinct and separate substance from the Jivas and the universe. The Qualified Monists hold that it is Brahman that has transformed Itself into Jivas and the universe. The Advaitins on the contrary maintain that Jivas and the universe have been merely superimposed on Brahman. But in reality there has been no modification in Brahman. The Advaitin says that the universe consists only of name and form. It endures only so long as there are name and form. When through meditation and other practices name and form are dissolved, then only the transcendent Brahman remains. Then the separate reality of Jivas and the universe is felt no longer. Then it is realised that one is the Eternal Pure Essence of Intelligence, or Brahman. The real nature of the Jiva is Brahman. When the veil of name and form vanishes through meditation etc., then that idea is simply realised. This is the substance of pure Advaita. The Vedas, the Vedanta and all other scriptures only explain this idea in different ways.
Disciple: How then is it true that Ishvara is an almighty Person?
Swamiji: Man is man in so far as he is qualified by the limiting adjunct of mind. Through the mind he has to understand and grasp everything, and therefore whatever he thinks must be limited by the mind. Hence it is the natural tendency of man to argue, from the analogy of his own personality, the personality of Ishvara (God). Man can only think of his ideal as a human being. When buffeted by sorrow in this world of disease and death he is driven to desperation and helplessness, then he seeks refuge with someone, relying on whom he may feel safe. But where is that refuge to be found? The omnipresent Atman which depends on nothing else to support It is the only Refuge. At first man does not find that. When discrimination and dispassion arise in the course of meditation and spiritual practices, he comes to know it. But in whatever way he may progress on the path of spirituality, everyone is unconsciously awakening Brahman within him. But the means may be different in different cases. Those who have faith in the Personal God have to undergo spiritual practices holding on to that idea. If there is sincerity, through that will come the awakening of the lion of Brahman within. The knowledge of Brahman is the one goal of all beings but the various ideas are the various paths to it. Although the real nature of the Jiva is Brahman, still as he has identification with the qualifying adjunct of the mind, he suffers from all sorts of doubts and difficulties, pleasure and pain. But everyone from Brahmâ down to a blade of grass is advancing towards the realisation of his real nature. And none can escape the round of births and deaths until he realises his identity with Brahman. Getting the human birth, when the desire for freedom becomes very strong, and along with it comes the grace of a person of realisation, then man's desire for Self-knowledge becomes intensified. Otherwise the mind of men given to lust and greed never inclines that way. How should the desire to know Brahman arise in one who has the hankering in his mind for the pleasures of family life, for wealth and for fame? He who is prepared to renounce all, who amid the strong current of the duality of good and evil, happiness and misery, is calm, steady, balanced, and awake to his Ideal, alone endeavours to attain to Self-knowledge. He alone by the might of his own power tears asunder the net of the world. " —Breaking the barriers of Maya, he emerges like a mighty lion."