The debate from a theistic viewpoint about the Big Bang centers around what happened before the Big Bang. Science wasn’t able to answer this before, and the theist would say that God created the Big Bang.
So, now we do have a complete mathematical modeling of the Big Bang. A somewhat lay article is here:
I had to do some digging, but here is the original paper which shows the proof:
To quote this paper:
“The problem of singularity can be avoided naturally as the universe can be spontaneously created from nothing.”
The authors of this paper deserve special mention. They are Dongshan He, Dongfeng Gao, and Qing-yu Cai. The hyperlinks take you to a search for other places on arxiv.org that they are located.