To prove it you have to provide a definition first. What axioms are you positing as prerequisite for God? It is hard to be consistent without that context.
And it should be bloody obvious that the requirement for proof is to establish a non-null prior for God. Without that prior the belief is, by definition, irrational. I, for one, am very careful about not making irrational assertions, though most of the population doesn't seem to have this impediment.