The Atma/soul is be believed to be infinite, opmipotent, omnipresent, pure, divine and perfect.
How/Why (in the first place) did it get stuck in the finite body and forgot its reality?
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Because there's atma - simply put, us, - and bhagavan - simply put, the God. It was like that literally since time immemorial, as clearly said in BG 2.12: Never was there a time when I did not exist, nor you, nor all these kings; nor in the future shall any of us cease to be.
Bhagavan, or, I would prefer to say, Ishvara, creates this material world over and over for those of atmas who wants to try out being Gods themselves and not be involved in relationships with him. So all-knowing, ever-happy, and totally-pure soul can fall into material life only by its own envy of God.
It's insanely hard to find out specifically in scriptures the clear explanation of reasons for creating this material world, but Krishna in Bhagavad-gita chapter 9 and chapter 12 explains in great details what he ultimately wants from atma. When individual atma restores the forgotten relationships with God it returns back to God and never falls back to material world again: After attaining Me, the great souls, who are yogīs in devotion, never return to this temporary world, which is full of miseries, because they have attained the highest perfection. (BG 8.15)
This confusion is created by the Advaita Siddhanta that claims that Everything other than Brahmam is Mithya (fantasy). According to Advaita there is no Jiva nor Prakruthi in reality. All these seemingly existing objects are unreal and appear so due to the delusion of Brahmam. Advaita deals with only Abheda Shruthi Vakyas as valid and conveniently forgetting the Bheda Shruthis and Gataka Shruthis. So, Advaita siddhanta cannot provide convincing answers to this question. So, is Dwaitam that holds the opposite views of Advaita ignoring Abheda Shruthis as invalid! Only Visishtadvaitam holds the key as it has all the answers as it accepts the entire Shruthi Vakyas as valid and true and procedes to explain all the Pramana Vakyas using Deha/Atma Bhavam concept. Accordingly, Jiva is distincltly different from Paramatma and also an eternal servant to Him. The conditioned soul (Baddha Atma) is going through the AnAdhi Karmic cycle of birth and death owing to its enticement in Samsara Maya of the created Universe forgetting its divine nature and proximity to Paramatma.