I promised I would address this. I'm not a believer in any organized religion ~ in fact, I'm strongly opposed to any legal protection for organized religions whatsoever. It is one thing for an individual to believe in something ~ to my mind, there is no justification for the "freedom of religion" to mean that any institution deserves the right to exploit that freedom.
Still, I don't shy away from the study of religions, as I don't have to believe to know how they work.
The "reality" of the gods has no effect at all upon the cleric's faith. Faith is much more than just believing in the existence of god. It is also believing in the agenda of that god, and that you as a cleric understand that agenda well enough to do god's work. As a piddling little cleric in an obscure part of the game world, you're not blessed with opportunities to speak directly to your god. You depend on writings which, however labeled perfect for the dumb masses, are a miasma of confusion for the devout cleric who doesn't want to fuck up and piss god off. You wish you had perfect clarity; what you have instead is faith.
Suppose you're a devout orcish witch-priest and your god Gruumsh, and you have a precious scroll written by Garnag the Excessively Pious that tells you, "Dwarves are hideous and all deserve death; to touch a dwarf is to be infected." This scroll tells you that Garnag received his knowledge of Gruumsh from a vision that was given to him on 37 consecutive nights, whereupon he wrote the holy words you're reading as a witch-priest exactly as the visions dictated.
Now, suppose you also have a scroll written by Othmash Who Died as the Gem of Gruumsh, which were the last 1,010 words of Othmash as he lay dying, having slaughtered 200 orcs before Gruumsh decided it was time to raise his spirit to the afterlife. And 17 of those words read, "The witch-priest of Gruumsh has no greater task that to remain alive until called to death."
Okay, got it? Now, here's the situation. You've gotten into a fight with a dwarf on a high place and unfortunately you've slipped on the poor ground and now you're hanging by your fingertips atop a 500-foot drop. And the dwarf, being a goody-goody, is reaching out his hand to save you.
You know from Garnag that you can't touch that hand, so you wait for Gruumsh to do for you what he did for Othmash ... but you don't hear a goddamn thing. And your fingers are getting tired. What do you do? What? Do you infect yourself with the Dwarf's touch or do you throw your life away before Gruumsh raises your spirit? Pick.
That's where faith comes in. The faith to guess what Gruumsh really wants you to do. Understand: if right now you're weighing the sacredness of Garnag against that of Othmash, you're choosing what you should do on the basis of two mortals, neither of whom are your god. Are you really going to put your faith in mortals at this moment?
Theology is full of these conundrums. It's what makes theology fun.
Now, I was also asked if spells are proof of god's existence ... and I suppose they are. That is a very minor point. The more important "proof" is that the god's giving of the spell to the casting cleric serves to remind the cleric that the god approves of the cleric's will. Think on that a moment. Your faith in your god, as the being that's got your back, is reassured every time you cast and the magic occurs. You live in terror of the day that you cast and nothing happens. On that day, you know you've angered your god by something that you've done.
So you make up your mind and you reach out and take the dwarf's hand. The dwarf hauls you up and then steps back, letting you catch your breath. Your godentag dangles from your wrist. The dwarf hangs his hand axe on his belt. Together you watch each other. Carefully, the dwarf lifts a small bottle hanging on a string from his belt and uncorks it. While he steals a drink, you decide to cast a quick cure light wounds on yourself.
How are you going to feel if the spell works? What if the spell doesn't? It matters.
It's a question of faith. Making decisions on the ground level that will please or displease a god that hardly knows you exist.
Chew on that for a while.