It’s a big question and there are many reasons to accept that he does.
Our universe had a beginning. So it seems reasonable that an eternal, ‘unmoved mover’ like God, created the universe.
There are objective moral values. Without an eternal law-giver, like God, we cannot say something like murder is absolutely and always wrong.
Yet the most convincing reason to accept the existence of God is that he has revealed himself - most profoundly in the person of Jesus Christ. Jesus was a real historical figure who did the works of God, acted like God, claimed to be God, and was resurrected from the dead by God.
So these reasons: causation, morality and revelation, give us good reasons to believe God really exists.
