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You cannot prove that there is not a Creator. Assuming the Big Bang theory (or any other universe-starting theory) is true, who created the matter that became the universe? Can anything create itself? Anything that exists was created.

You can't prove there is one.
Existence is, and always has been. There is no creation, only change and transformation.
Nothing can create itself. The fundamental principle of existence is the distinction. In order for there to be nothing, there must be a distinction between nothing and not-nothing. But a distinction is different than nothing, and so Nothing is not a possible state of existence globally (although it is possible locally.)
If anything that exists was created, then God was created, since he also exists. Of course, that raises the question, "Who created God?" And whatever answer is given to that question is subject to the same question, "Who created that?" There is no transitive closure to that sequence of questions and answers--which is why reality must be eternal.

"If anything that exists was created, then God was created, since he also exists."

That's not good logic.

"In order for there to be nothing, there must be a distinction."

No. If there is nothing, then that's all there is. It's called the empty set. The quantity of all things that exist is zero.

"The fundamental principle of existence is the distinction."

Distinction is a concept, and regards the fact that individual things that exist can be differentiated. Distinguiability occurs when the first thing other than nothing exists.

You can't prove there is one.

The establishment of a Supreme Being precedes your accusation that there is not, going back thousands upon thousands of years.

1 + 1 does not equal 2. Prove to me that it does, then prove to me that the number "2" is the correctly applied name for the result of 1 + 1.

Existence is, and always has been. There is no creation, only change and transformation.

Then how do you explain motion? Motion doesn't create energy. It receives energy from its mover. If there's no first mover, there's no energy. If there's no movement, there's no time. There can be no change or movement (time) without an external force that sets it in motion.

Nothing is not a possible state of existence globally

Which is why before the universe was created by God, there was void. Since God is not a corporeal being, void is not evidence against the eternal existence of the first mover.

There is no transitive closure to that sequence of questions and answers--which is why reality must be eternal.

Reality is limited only to what man can sense or reason? Wow. Is gravity a reality?