The important thing to remember is that non-deists don’t have to “prove” evolution or anything at all.
The Anti-Evolution creationists beef with the theory of evolution is that it kills off what for millennia was a killer argument for the existence of a divine being - intelligent design.
In a theological setting, the point isn’t whether the theory is demonstrably correct but that it posits a plausible alternative explanation for what had previously been considered only explicable by positing a divine creator.
If you let them make it an argument for you proving that evolution is correct, you’ve let them choose their only remaining ground.
The point is that they need to explain why “God did it” is the only possible answer despite evolutionary theory. And they can’t. They can only try and claim that the theory is wrong. Which they also can’t do (they can assert it but all their arguments so far are rubbish).
The savvier religious denominations have understood that and folded evolution into their theology by saying “Yes, evolution but that’s how God did it.”
Darwin basically handed them that path in the closing paragraph of The Origin of Species:
“Thus, from the war of nature, from famine and death, the most exalted object which we are capable of conceiving, namely, the production of the higher animals, directly follows. There is grandeur in this view of life, with its several powers, having been originally breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.”
I have no religious beliefs, and that passage fills me with awe every damn time. Any half-awake clergy should be able to weave that into a decent sermon about God’s wonders, and many did. The others … they puzzle me, and I don’t trust them at all.