God cannot be proven using logic anyways. If you actually think God is a beeing that can be explained and proven by logic, then tell me:

If God is omnipotent, can he create a Stone so heavy that he cannot lift it?
If God is omnipotent and caring like a father, then why does evil exist?
And if God is not omnipotent, how is he God?

God can only exist outside of all human logic.