When is God's birthday?

If you're referring to the God of Judaism, Christianity and Islam, this God (the only God) has no birthday. A birthday requires and refers to a point in time, but God does not exist within time, as everything within our universe does. If you exist in a dimension/place where there's no such thing as time, then you have always been, and you always will be. (Hence when Moses asked God, "What is your name? Who shall I say sent me?" God answers " tell them 'I AM' sent you", indicating mere existence based on nothing except himself.) By definition, God is uncreated, independent, uncontentious on any per-existing matter or energy. All matter in the observable universe (atoms, galaxies, human babies) was formed by and contingent upon some already existing matter, energy and force. God preceded these things, and is the creator and maintainer of matter, energy and the four forces which govern them. He is the eternal Fact from which all else springs.

Of course Christians believe God was born into time on Earth temporarily in human form. That birthday's been narrowed down to sometime around 12-25-00.

Nobody knows God's birthday.