I still puzzle over that one. :) Why can't we just say that God is the author and creator of everything ELSE that exists, but not Himself? I would think that God exists because we can say for sure that there is that which is God (concretely, more than a mere idea) and there is that which is not God.
Because English is such a lousy language for Christian theology, maybe we can say that if we recognize how completely wrong it is. :) The Greek words used for God on icons are Ο ΩΝ, which as near as we can say in English means "The Being which created Beingness" Bottom line, FK, the source of "existence" is God; God gives us existence but He Himself does not exist nor is He existence itself. Look at it this way, God is the source grace and that grace falls on creation like rain on the earth, but God is not grace nor is He "graced". Grace, like existence, is a manifestation or emination of God.