The theory of relativity does not go against logic. In fact it is based on mathematical logic.
I agree, but you miss the point. Unless you understand the math, which most ordinary people won't, the effects of relativity seem go against our common sense intuitions and prima facie ideas of logic. My whole point here is, this is an example of something seeming to go against logic when you don't have all the information. I think this is what is happening when you say the universe has a beginning and then conclude God. You do this when lacking all the information, information that could explain why there is something rather that nothing without God, even though such an explanation might presently go against your common sense ideas of logic.