We have evidence. Your problem is that you want proof, and you don't see the difference.
We have written evidence. It starts with the Bible, and extends to the writings of many, many Christians over the last couple of millennia. I once helped a library shelve a full collection of the Greek and Latin Patrologies, and believe me, it's a lot of shelf space! And you can find more, in libraries and bookstores.
We also have evidence that isn't written, just passed down among us. And evidence from our own experiences.
Now, all the evidence is subjectively selected and interpreted. That's what happens if there isn't any proof. That's the case for atheists' evidence, too (even when it's proof of something else, like the proofs of evolution or the Big Bang). As evidence for the nonexistence of gods, it's subjective.
As far as I can tell, from reading the sources, the "theists believe with no evidence" notion was a rhetorical scam introduced over the last couple decades by New Atheist writers. They deliberately replaced "no proof" (which would have been true) with "no evidence" to dodge an obvious hole in their own arguments: that they haven't got any proof, either.