Out of nothing
You are completely wrong in your essay about the creation of the universe. The big bang does prove that God exists. The big bang had to some from somewhere, and it couldn’t have come from the universe because something can’t come from itself, so it must have come from something that isn’t the universe, God.
You are using two different definitions of the word “universe” here. There’s our universe, which is what started with the Big Bang, and there’s the entire universe, which encompasses all natural things that exist. Our universe may have been the result of something in the entire universe, making God unnecessary.