To me you are dancing around.
You say "at no point was there no time, no space, etc"
You are saying it all started with the BB but yet if
"at no point was there no time, no space, etc" then the BB couldn't have started unless it was proofed into ignition so to speak. IMO
You are thinking of time as outside of the universe. That is a mistake. Time is part of the universe.
The south pole does not 'poof' the Earth into existence. The Earth exists and the smallest latitude is at the south pole. Similarly, the universe of spacetime exists and the earliest time was at the BB. There is no 'before' to 'poof' from. ALL existence is at or after the BB (in the BB model).