I have answered similar questions earlier also. No doubt, Atman is infinite and beginnless, so Can there be any beginning or ending of infinite?
Chandogya Upanishad 5.1.1
ॐ । पूर्णमदः पूर्णमिदं पूर्णात्पूर्णमुदच्यते । पूर्णस्य पूर्णमादाय
पूर्णमेवावशिष्यते ॥ ॐ खं ब्रह्म । खं पुराणम्; वायुरं खम् इति ह स्माह
कौरव्यायणीपुत्रः; वेदो'यं ब्राह्मणा विदुः; वेदैनेन यद्वेदितव्यम् ॥ १ ॥
इति प्रथमं ब्राह्मणम् ॥
- Om. That (Brahman) is infinite, and this (universe) is infinite. The infinite proceeds from the infinite. (Then) taking the infinitude
of the infinite (universe), it remains as the infinite (Brahman)
Chandogya Upanishad 7.23.1
- Sanatkumāra said: ‘That which is infinite is the source of happiness. There is no happiness in the finite. Happiness is only in
the infinite. But one must try to understand what the infinite is.’
Nārada replied, ‘Sir, I want to clearly understand the infinite’.
- Sanatkumāra said: ‘Bhūmā [the infinite] is that in which one sees nothing else, hears nothing else, and knows [i.e., finds] nothing
else. But alpa [the finite] is that in which one sees something else,
hears something else, and knows something else. That which is infinite
is immortal, and that which is finite is mortal.’
A person trying to understand Aatma should practice righteousness first like Yama, Niyama that are like non-violence, non-stealing, non-lying, continence, Satvik diet etc.,. Because Aatma is not some third person nor some bookish theory, but the first person, the Self. How can the Aatma, which is pure truth can establish in a person who is egoistic, liar, sensuous and atheist person? For a satvik deserving sadhaka even the Mahavakya 'Aham Brahmasmi", "I am Brahman/God" is enough for self-realization, but for a tamsik fool entire Vedas, Vedanta, Puranas, Geeta etc., and even eternity is insufficient hence reincarnation or resetting of jiva by Prakriti is needed and renunciate Sanyassa Ashrama and Brahmin Varna devoted in understanding Aatma were formed in the ancient Vedic society. That was the difference between a Asura Virochana and Deva Indra when both tried to understand Brahmgyan from Prajapati.
Chandogya Upanishad 8.7-12
Once Prajapati, the creator of the universe announced, “The Self is
the sinless, ageless and deathless One; it has no sorrow nor hunger
nor thirst. The goal of all its desire is the Truth, Truth is the one
thing worthy of its resolve. It is this Self that has to be sought
after, it alone one should seek to know. And one who seeks after the
Self and knows it, gains possessions of all the worlds, wins all that
Both the gods and the demons heard this announcement and thought, “We
must know this Atman or Self and seek this knowledge that promises all
worlds.” Hence, Indra, the king of the gods and Virochana, the leader
of the demons, approached Prajapati with all the humility of a
disciple and requested him to impart this knowledge to them. Prajapati
accepted them as his disciples and asked them to stay with him for
Both, Indra and Virochana, stayed on living the life of a Brahmachari.
At the end of that period, Prajapati called both of them and said,
“Dear ones, the person visible in the pupil of the eye is Atman. This
Atman is the Brahman, the immortal and fearless. Go and see yourself
in a pan of water and then tell me what you saw.”
Next day when Prajapati asked both of them to narrate their experience
they both said, “Lord, we saw the Self entirely as we are, the very
image even to the very hairs and nails.”
“Go and adorn yourself and then look into the pan of water and tell me
about your experience” said Prajapati to both of them.
Happy, they went and adorned themselves, looked into the pan of water,
came back and replied to Prajapati, “Revered Sir, we saw ourselves
well dressed, well groomed and well adorned.”
“Very good, this is Atman, the immortal and fearless, the Brahman”
thus confirmed Prajapati to them.
Both Indra and Virochana, went happy and very much satisfied in their
heart. Prajapati saw them going away and exclaimed to himself,
“Whether they are gods or demons they will inevitably perish if they
are satisfied with the mere reflection of the Reality.”
> Virochana went to the demons and taught them this knowledge by saying
that this bodily self is all that we need to know and serve and
glorify. This is the supreme knowledge by which one obtains the world
here and hereafter.
Indra was different from Virochana. He realized that something is
wrong with what he has just learnt about the Atman. He felt uneasy. He
thought to himself that as the water reflects a well adorned body so
does it reflects a blind man if he is blind, a defective man if he is
defective. If a body is destroyed or dead, then there is no reflection
of a living body. How then could the body or its reflection be said to
be the deathless Atman?
He went back to Prajapati and said, “Lord, I see really nothing worthy
in this body or in its reflection. Please give me the true knowledge
about the Atman.” Prajapati was happy with Indra and asked Indra to
stay with him for another thirty-two years. At the end of that period
Prajapati called him and said, “That which moves about in dreams is
Indra seemed to be satisfied and made his way to the abode of gods.
But as he went along, again doubt crept into his mind and he thought,
“How can the dream self be Atman? In dreams one suffers, one is
wounded, one weeps when afflicted. The fearless and sinless Atman
cannot be subject to such happenings. This does not seem to be the
truth. Even this time also something again is wrong with what I have
learnt.” He came back and prostrated himself before Prajapati
requesting him to explain the truth of Atman.
As usual, Prajapati told him to stay with him for another period of
thirty-two years. Indra was all prepared. At the end of this period,
Prajapati called Indra and said: “The self who is full pleased and is
in a happy mood in deep sleep is the Atman.”
Indra was satisfied and went home. But before he reached his place,
again doubt overwhelmed him and he said to himself, “In a dreamless
sleep, the self does not know itself. It is not conscious of its own
existence. How then can the unconscious self be Atman when it is
described as the ever luminous one, ever conscious one?” He came back
again to Prajapati and reported to him about his difficulties. This
time Prajapati was more pleased with Indra and told him to spend five
more years with him.
After the period was over Prajapati called Indra beside him and said:
“O Indra, you have deserved the knowledge of the highest truth by your
persistent effort and intense inquisitiveness.” Saying this Prajapati
revealed that part of the highest knowledge to Indra for which he was
ready at that point of time.
“This body is subject to death yet it embodies the deathless and
bodiless Atman. This embodied Self falls into the trap of all
dualities like pleasure and pain, but the bodiless Atman is not
touched by any duality. So long as the Atman resides in the body and
attaches itself to them he seems limited and restricted, but again
when freed from the body becomes one with the infinite spirit. When
the Atman leaves the body, goes wandering freely in the infinite
worlds. The eye, the ear, the senses, the mind are there only in order
that the Atman may see and hear and think. It is on account of Atman
and in the Atman that the things and beings exist. He is the Truth and
the final repository of all existence.”
This time when Indra went back to impart this knowledge to the gods,
he had no doubt. The gods received the true knowledge and therefore
live in the full knowledge of their Self. And because Virochana was
satisfied with the knowledge of body as self, the Asuras, even today
live in the ignorance taking body as Self.
What one thinks one becomes, thats why King Bharata had to take an extra birth of deer despite becoming an ascetic, because of constant thinking of deer at the time of death. Thats why Ramkrishna Paramhans inherited feminine traits because of constant thinking and worshipping of Devi. A jiva thinks itself to be body made of matter and doer and enjoyer of actions in false ego thats why he undergoes reincarnation. One who realizes "Aham Brahmasmi", "I am that" alone is eventually freed.