So how does cosmic expansion, background radiation, and nucleosynthesis prove that there was a big bang? It proves nothing. I theorize that reverse gravity is pushing the galaxies apart, while at the same time maintaining normal gravitational effects. You can't disprove it either, and it is just as credible as any other theory out there.

Background radiation? There should be that, but it doesn't prove the big bang. Just because the radiation lessens the further out the universe goes doesn't prove there was a big bang.
In fact, it proves that my theory of reverse gravity is more likely due to the almost uniform distribution of the radiation.

Nucleosynthesis? It only lasted for seventeen minutes? Ok, who timed that, and what kind of watch did they use?

Not trying to be an a** about this, but if you read the explanations on these things the usual comment is "scientists believe". That simply means they don't know, but have to put something out there. Faith is on both sides.