In fact, even if the whole world happened to agree with the Nazis, their actions would still be objectively evil.

How would you know? If the whole world "agrees with the Nazis" - by which you must mean approves of their genocide - then you, being part of the world, would agree with them, too. So how could you say otherwise?

You are not talking about "objective" morality; you are talking about transcendent morality that exists independently of whether anyone recognizes it. Yes, we'd need a God for that. But we don't need transcendent morality. We need objective morality, which is just another word for game theory in the massively multiplayer iterated prisoners' dilemma we call being human.