Mathematics and physics are two distinctly different fields. Mathematics works well to describe many, if not most, aspects of physics, but not all. Mathematical singularities work well to describe many physical things, but not all. You can mathematically describe a trumpet like shape with finite volume but infinite surface area - you can fill it with paint, but there is not enough paint inside it to paint it, even thought the wall thickness is zero. The trumpet is simple. It has a radius, 1/x, that asymptotically approaches zero along its length, x. Such is life with math.
I don't believe the Big Bang could have ever started with all mass in the universe squeezed into a volume of zero. That's not possible with physics. It may be convenient to describe this as such a singularity, and the mathematics may work out just fine with such an assumption, it is nevertheless not possible. In fact, the mathematics don't work out 'just fine'. The 'Big Bang' physicists require the "inflation" period (during the transition from mathematics to reality) where "the laws of physics didn't apply". Could this may have required a little help from "the hand of God"?
If one is predisposed to not believing in God nothing will prove Gods existence. Although I met a former atheist who came to believe in God after he found himself dangling off a rock face very high up and calling on God to save him...he was perplexed...”why am I calling on someone who I KNOW doesn’t exist?” His demonstrated irrationality caused him to address his opinions and beliefs.