The basis of their belief is the supernatural. The supernatural doesn't require anything other than their belief to support it.
And notice believers didn't come up with these ideas on tehir own, they learned about them from those around them in their social experience. Is it Hindu gods they believe in? Or a Eastern Orthodox version of God they believe in? Or a Muslim version o God they believe in? Or Shinto divinity? Or Native American spirits?
No one hears about Native American spirits existing in the Middle East. Japan's traditions don't include Jesus.
Lets say you successfully attack one belief. Another belief can easily appear in it's place. For example, used to be all non-believers go to eternal hell. You point out how unfair this is. So hell now becomes a temporary place, or you, the non-believer misunderstood the meaning of hell.
Well as far as we are concerned a hell doesn't exist outside of the Christian tradition that spreads this idea. And it's notable that Christians never are the one's destined for hell, it's only for others. That's a little self-serving and fishy.
While I've used the same argument myself for my lack of belief, I find most believers feel that God has somehow influenced their life which wouldn't be the same if God didn't exist.
Was it actual gods, or just the social traditions that include ideas of gods? It's important to examine the emergence of gods in human civilizations, and what purpose they played for the culture. Most all modern versions of religions ignore the early formation of their religions and focus on a story that has evolved to some form. Catholicism is vastly different that protestant forms of Christian belief. For example Catholicism values Mary, and in protestant forms there's more value assigned to the Old Testament and paul's writings.
Signs is a big one. Something happens, they see it as a sign from God. They base a decision on this sign. They feel their life has improved because of the sign God sent which they listen to. Without the sign they would have made a different decision which would, of course, made their life worse.
Sure, some believers need reininforcemnet for their belief and faith. These are ideas that aren't based in fact, and faith is notoriously unreliable, so signs and symbols are important to indicate God exists and is communicating. A believer might see Jesus in a piece of burnt French Toast. How do they know it's Jesus? The mages I have seen look like caucasian Jesus with long flowing hair. It seldom looks like a Middle Eastern fellow, which is what Jesus would have been.
There's a very good movie called
Henry Poole Is Here. Part of the plot is an image that appears on the main characters garage wall and he doesn't believe, but his neighbor does, and she invites people to come and see the image. Henry has reasons to be angry due to a bad medical condition, and he ends up destroying the wall. In the end his fate changes with a clever plot twist. The thing is the sign was about how others have faith towards others, and isn't really about the sign his neighbor sees. Luke Wilson does a superb job.
Since you can't have them go back in time to have them make a different decision, you can't prove otherwise.
All folks need hope at some point. Some need it all the time.