All rational beings believe in their own existence, whether or not they actually exist. Sherlock Holmes believes that he exists, but he is wrong. God too believes in his own existence–and his omniscience makes it impossible that he is mistaken. Therefore God exists.
On the other hand: Perfection is essential to godhood, and a perfect God must be perfectly virtuous. But virtue implies overcoming pain, fear, and temptation, and a God who is subject to these ills is less perfect than one who is not. Thus perfection is impossible, and God cannot exist.
Asked what he would say to God on Judgment Day, Bertrand Russell said, “Not enough evidence, God! Not enough evidence!”