Saying that God exists as a religious idea would be a move in a sophistical word game, though. God is supposed to exist as the source of the universe, according to monotheism. Could an idea in religious people's heads have created the universe? No, so that's moving the goal posts and playing with labels.

But sure, God couldn't exist in the way that natural things do. God would be more like Being itself than like any particular being. But that amounts to saying that God doesn't merely exist at all.