the most reliable math of physics says T-0 is inevitable
The part that you aren't getting is that the alleged singularity at t=0 is an illusion, a simple horizon effect.
Here, let's walk through it gently. If you take the Hubble expansion, and work it backwards, then 15-16 billion years ago you arrive at a point where your math stops working. If we try to conceptualize this theoretical point, we end up talking nonsense about infinite density. What we appear to be describing, at that point, is the most awesome black hole ever. And, as you know, nothing actually gets out of a black hole. So, clearly we have to stop short of there, the earliest times we can describe will be after that.
Quantum physics looks at these earliest describable times, and notes that in such a situation, every possible field in the standard model would be doing its thing in one place at one time at very high energy levels. Under such circumstances, the field with the greatest range will win. This was a scalar field, similar to the one that currently causes Hubble expansion and perhaps to the one(s) that hold matter together in such a way that it takes up space and has mass and is stuff.
So nevermind t=0, let's start at t=1 with such a high-energy field face off. No singularity required, this could be happening in any sort of universe, prior conditions remain pretty unguessable (though the superstring guys are doing their damnedest.) So then at t=2, what we now call the observable universe is 3-5 billion light years in diameter and almost perfectly evenly distributed. Nothing exploded, there was no bang, space itself went through a quantum leap of expansion which shredded any matter and energy there might have been into virtual nothing and then degenerated into the normal expansion we get now, a lower-energy field state.
This process is called Inflation, it currently owns and operates the proprietorship of its parent company, the original Big Bang. Now if we go back to the Hubble expansion, and work it backwards again, this time only to the point where we have a nice 3-5 billion light year universe, we get back to around 13 billion years ago. Do you get that? While t=0 was supposedly 15-16 billion years ago, and also patently impossible, t=2 is only 13 billion years ago. t=1 is such an awesome event, that it can keep its name, because whatever was going on "before" that remains indescribable. But t=0 never was, nor will it ever be.