We Never Know
No Slack
The point is that abiogenesis does not describe a process, it is just a term for the transition from no life to life, however it took place. It's not a matter of it being "proven". If one accepts that once there was no life on the Earth, then abiogenesis occurred, because now there is life. How abiogenesis occurred is the interesting subject.
It's not the Big Bang that breaks down at a certain point. The Big Bang is a model for the very early stages of expansion of the universe, based on extrapolating from observations of the cosmos. The extrapolation can't be extended right back to what looks like the start because the laws of physics break down at a certain point. So the Big Bang does not attempt to describe the start, if there was a start. The Big Bang describes what seems to have happened from a point shortly after that.
None of this has any relation to whether or not there may be a higher power or being. This is just science. "God of the Gaps" (a phrase coined by one of the professors whose lectures I attended at university, and who was a Methodist lay preacher) is a lousy basis for faith in a supernatural power.
God of the gaps - Wikipedia
I disagree. Abiogenesis is the natural process for the origin of life. No god needed.
Of course the BB itself doesn't break down, the study of the BB breaks down.