On the topic of proving God exists, there are many ways that people just don't bother thinking about. I could go philosophical and say, if you believe man created this and that, then it is only possible to say that someone created nature as well, seeing that one thing can only be created by another. Nothing just 'happens'. That is the elementary thinking of monotheism, not just the Catholic or Christian god. Nietzsche is wrong! Now go look up who Nietzsche is.
Jesus may have had a brother named James. It's a very slim chance she and Joseph did not have another son for the rest of their life. And she didn't have intercourse with God! God doesn't need to do that. He says 'have a son' and you will. He's God.