The big bang singularity idea is just that extrapolating backwards from what we can see now, the universe must have a beginning.
As opposed to being eternal and overall being in a 'steady state' .
There is no evidence I know of suggesting that the latter is true, but plenty supporting the first.
'Singularity' is another way for saying 'the math stops making sense here and we don't really know what happened'
A mathematical singularity does not describe a physical object, it describes conditions which we currently don't understand, (although ideas abound, bouncing universe, various kinds of recycling universe, A universe with 28 dimensions, ...)
At one point I Iiked the idea that what goes into black holes is the same thing we see as the big bang, but apparently that doesn't work because these two singularities have different qualities, one is a time-like singularity and the other is 'spacelike', and apples are not oranges.