why go back to just the big bang, certainly something caused the big bang...

There is no reason to assume a causal principle.

why do we think TIME started at the moment of the big bang?

Because that is when the dimension of time unfolded became greater than zero length.

there is no reason not to...

how do we know that time unfolded then?

Actually there is a reason not to. Many people have a very hard time accepting it.

I think therefore I am is false. You can not get to I am from thinking without an assumption of a causal principal. The rest of the things you need you can prove mathematically, but you have to assume causality.

Here is the rub, If an artificial intelligence is capable of thinking, then you disprove causality. This because of a computing law about a program running on a simulator being unable to tell if it is running on a simulator or on real hardware. Hence thinking is unable to tell if it is a simulation or real.

This leaves us with: I think, therefore there is thinking. And you and the world cease to be real. Besides with the Heisenberg Uncertainty Principle we are at best a probability function. So it all neatly falls into place and we can not prove ourself to be real, but we can't exclude reality either.

It is kind of circular, but until time unfolds, there isn't time. Therefore it did not exist before that. However I think you are trying to say that the other dimensions - X,Y,Z - unfolded after time. I'm not aware of a theory that has them unfolding at a different point. Perhaps that is inflation. I can't do the math.

Sounds nihilistic.
Anyway, which math can't you handle? Seems you've handled it well enough whenever you bring it up elsewhere.