Could an enlightened or awakened being believe in the existence of a God?
Awakened - yes. Many awakened people believe in God. They don’t call it God, usually, they give it different names. The Source, Godhead, the higher self, infinity - many names.
In self-realization you merge with God and realize your godliness. God is existence, God is love, these words are synonyms. It is nothing more than a symbolism for your own infinite love to yourself as a living being. For as long as you feel like there’s you and there’s God, you don’t know yourself, you have not yet known your godliness. To say “I am God” is to say “I am not, he only is”.
In enlightenment, God is transcended into something much deeper. God cannot be alive, he’s too perfect to be. He can only be dead, only in nothingness the perfection is possible. To transcend God is to realize one’s own non-existence, one’s own emptiness. It is to dissolve into the unfathomable serenity of accepting the unspeakable eternity of death and to return to utter ordinarity.
So, no enlightened being believes in the existence of God. Man created God out of fear of reality. To believe in God is to reject death, and to reject death is to reject life.