Is the Big Bang God’s Way of Proving His Existence?

Yes, it could be.

I personally believe the “big bang” describes the moments when God said, “Let there be….”

Scientists will never be able to prove or disprove the existence of God, simply because God created the big bang. It is like me creating a big baloon, and sticking an ant inside of it on a rock (the balloon is like the universe, the rock like earth, and the ant represents humans). The ant will never be able to prove I exist or don’t exist, because all it will ever be able to see is my creation and its surroundings within the mini universe or dimension I created it to live in.