Literally what you are saying is that if everyone believes that God exists, then he exists.

You're right; "universally convincing" was a mistake. Actually, the revelation need only be convincing to the atheist who is saying there is no God. He says There is no God," and then God appears before him in a burning bush that is not consumed and tells him to go free his people. (Passover's coming.) So, the atheist is convinced that he was wrong, because a counterexample was provided to his satisfaction. The burden of proof was on the theists, and they carried it because a counterexample was available.