It wouldn't surprise me one bit if the pope is an atheist. He, of all people should have excellent insight into how hollow the church really is. That's no reason to shut down a profitable racket though.
So he doesn't need to show you the science behind what he was saying, he can just show you the math behind the bookkeeping.
I remember a radio interview with a priest (can't recall which denomination) who did the six years to get his doctor of divinity. He said that after learning about the history of the church and the various schisms and how the bible was formed, that there was an in-joke that went 'if after six years of divinity school, you still believe in [the christian] god, you weren't paying attention'
I find it a fascinating exercise in radical empathy to try to imagine what the pope's mental world is like. Mind you, I think I pretty much fail utterly.
What I have read of the writings of the people that the Catholic church venerates, especially from pre-modern times, I find they strongly smack of sincerity when they talk about metaphysics (like resolving theodicy, or the "limbo of the infants", etc). They argue so passionately, and in such convolutions. And people have chosen to be burned at the stake, just to avoid saying "Yeah, you're right, I was wrong about God, I take it back." Those people, at least, must really believe, at a profound level.
Mind you, I find that they strongly smack of insincerity and self-service when they talk about worldly matters, like excommunicating kings for applying new taxes, or taking sides in WWII, or the whole condom thing, or dealing with accusations of pedophilia, or....
Such a surprising juxtaposition. Other churches seem to me to exhibit similar patterns, although few western religions have had a chance to build up such a legacy as the Catholic.
It's consistent in its inconsistency. If enough people believe it they say it then it must be real. But I don't believe it works like that (yes, that's just another belief). For those who would not take back that they were wrong about god there were also a few people that did not believe at a very profound level and that refused to take it back.
What would happen if a pope (no capital, and it's not a typo) would abdicate saying they no longer believed? Or if a pope would attempt to dismantle the church and spread their belongings amongst the poor?
So he doesn't need to show you the science behind what he was saying, he can just show you the math behind the bookkeeping.
And you too will come away a believer ;).