GOD exists because we believe He exists.
Think about it like this:
Reality is constructed through enaction. God is just as real to a priest as numbers are to a scientist. A scientist can show you his bridges, his computers, his particle accelerators, but to someone who is illogical and cannot count, they will only appear magical.
A Pastor can show you his churches, his followers, his books, but to someone with zero spirituality immune to profoundness or divinity, they will only appear deceptive.