I have heard this idea which I think it comes from the Upanishads. Can anybody give a a reference in the Vedas, Gita or any other literature from Hinduism in which existential ignorance is explained.
The universe was created by single consciousness by its reflections just like one Sun reflects into million reflections in million pots filled with water. So does One Paramatma(Supersoul) reflects/divides into infinite Aatmas(souls).
Eko ham, bahu syam - Vedas
I am one, let me be many
Just like a seed produced from a tree is a potent tree and contains a subtle tree so does every conscious organism of universe contains the potent hidden God.
The Rig Veda samhita 1.164.20-22, Mundaka Upanishad 3.1.1-2, and Svetasvatara Upanisad 4.6-7, speak of two birds, one perched on the branch of the tree, which signifies the body, and eating its fruit, the other merely watching. Rig Veda samhita says:
1.164.20 Two birds associated together, and mutual friends, take refuge in the same tree; one of them eats the sweet fig; the other abstaining from food, merely looks on.
1.164.21 Where the smooth-gliding rays, cognizant, distil the perpetual portion of water; there has the Lord and steadfast protector all beings accepted me, though immature in wisdom.
1.164.22 In the tree into which the smooth-gliding rays feeders on the sweet, enters, and again bring forth light over all, they have called the fruit sweet, but he partakes not of it who knows not the protector of the universe.
The first bird represents a Jiva, or an individual self, or soul. She has a female nature, being a shakti, an energy of God. When the jiva becomes distracted by the fruits (signifying sensual pleasure), she momentarily forgets her lord and lover and tries to enjoy the fruit independently of him. This separating forgetfulness is maha-maya, or enthrallment, spiritual death, and constitutes the fall of the jiva into the world of material birth, death, disease and old age.
The second bird is the Paramatman, an aspect of God who accompanies every living being in the heart while she remains in the material world. He is the support of all beings and is beyond sensual pleasure.
When the soul identifies itself with matter/mind and body and its ego, it is called feminine Jivatma/Shakti but when the same soul identifies itself with the Higher Self/Brahman and calling world to be a dream, it is masculine Paramatman/Shiva. Hence, some Samkhya Yogis, Advaita Gyanis like Kapila, Buddha, Mahavir identifying themselves with higher bird and one with Brahman denies existence of God while Dvaita Bhakts who identify themselves with lower bird describe God for God can be only seen from divisible feminine material realm not from the formless One masculine realm.
Sri Rama asked Hanuman a question in the assembly: 'O Hanuman, what do you think of me in relation to yourself?' Hanuman's tears were rolling down his cheeks. Full of love and tainted with Gyana he said, 'O Lord, when I think that I am the body (like when you think you are the body) then, Lord, you are the Almighty and I am your servant. O Lord, when I think I am the jivatman, the conscious, separated individual, then I am part of you, I am a part manifestation, I am your power. O Lord, when I think that I am the Atman [universal soul or consciousness], I am Thyself; when I realize that I am the Atman, you and I are one.'
So, the exact relation between God(universal consciousness/Supersoul) and an individual(local consciousness/Soul) is Achintya Bheda-Abheda which is an amalgamation of Dvaita and Advaita where the cause of difference is the individual's abstract ego and mind. Loss of ego and mind either through any of the Bhakti, Gyana, Karma, Yoga paths leads to Oneness in Samadhi which is beyond material realm.
In the beginning this was Self alone, in the shape of a person (Purusha). He looking around saw nothing but his Self (Atman). He first said, "This is I", therefore he became I/Aham by name. — Brihadaranyaka Upanishad 1.4.1
Na Tasya Pratima Asti - He has no image - Yajur Veda 32.3
Just like your soul, mind, intellect and ego are formless as this is the part of your consciousness, so is the masculine aspect of cosmic consciousness Brahman is also imageless and formless like infinite space. The one that takes form is feminine Prakriti/Shakti also called matter/energy in modern science. Forms exist to teach formless. How can a formless small consciousness(Drop) learn and understand about universal consciousness(Ocean) without Prakriti and its mind, love, intellect and matter and learn to live in harmony with Omnipresent, Omnipotent and Omniscient infinite consciousness. Hence, the conclusion "Sarvam Khalvidam Brahman-Vedas", everything is Brahman. Purusha is Prakriti and vice-versa.
The jnani gives up his identification with worldly things, discriminating, 'Not this, not this!' Only then can he realize Brahman. It is like leaving the roof of a house by leaving the steps behind, one by one. But the vijnani, who is more intimately acquinted with Brahman, realized something more. He realizes that the steps are made of the same materials as the roof: bricks, lime, and the brick-dust. That which is realized intuitively as Brahman through the eliminating process of 'Not this, not this' is then found to have become the universe and all its living beings. The vijnani sees that the Reality which is nirguna, without attributes, is also saguna with attributes.
Bhagavad Gita 9.4 This entire cosmic manifestation is pervaded by Me in My unmanifest form. All living beings dwell in Me, but I do not dwell in them.
Bhagavad Gita 9.5 And yet, the living beings do not abide in Me. Behold the mystery of My divine energy! Although I am the Creator and Sustainer of all living beings, I am not influenced by them or by material nature.