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Alex, I think your understanding is correct.
The maths, worked backwards gives the theoretical notion of a singularity.
As to your question: In reality the bottom line is we don't (perhaps can't) know and are merely speculating as to the state(s) at the early time scales. And the level of speculation goes up (perhaps exponentially) as time t approaches the theoretical singularity.
In my opinion terms like "primordial atom" are designed to provoke emotions.
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