Could you expand on this? I'm not sure I understand what overwhelmingly strong points you might bring up that your opponent might agree with. Would this be something like priest scandals? Or not having your prayers for understanding answered?

The one I mentioned about the Holocaust would be my go-to example. But really what's important is that it's not something completely intellectual they're going to have a cached response for.

On a side note, I've never understood people who use priest scandals as evidence for atheism. It seems totally ad hominem - "some of the guys who talk about this God stuff are bad people, therefore it's wrong". I guess you could get there by saying that if God existed He wouldn't allow such evil among His followers, but the only possible response to that would be "And where have you been for the past five thousand years?"