We've derailed a bit away from the evidence, to understand the theory better. This is fine, because it has been my experience that once they understand it, many people accept ToE, because it just makes so much sense. If you've got variation, and you've got selection, it's hard to see how it wouldnt' happen. Or, as T.H. Huxley is said to have said upon hearing it, while slapping himself on the forehead, "How extremely stupid of me not to have thought of it myself." So this discussion is good.
However, I did promise evidence, so will continue. [as so often happens, creationists have little interest in it. I think they find it easier to deny its existence if they don't look at it.]
So far I think we've had the age of the earth, and nested hierarchy of life. Next: DNA.
It's important to remember that Darwin knew very little about genetics. Mendel's work had been temporarily lost. He had spent a lot of time talking to pigeon breeders, so understood the nuts and bolts of breeding. But no one at that time knew anything about what causes offspring to resemble their parents. For ToE to work, there has to be some mechanism that causes organisms to reproduce inexact copies of themselves, and this mechanism should be the same for all organisms.
I think you can see why there has to be such a mechanism, because ToE is premised on a range of slightly differing offspring that natural selection is going to work on. As to why it should be universal, remember that ToE says that all life on earth is descended from a single ancestor. Whatever it is that got that ancestor to replicate, is the thing that is passed down through all of Biological history.
Also bear in mind that although we know about DNA now, there's no necessity for reproduction to be based on it. There could have been some other kind of self-replicating molecule, some other basic mechanism for reproduction.
But there isn't. 100 years after Darwin's work, we came to understand the mechanism that causes descent with modification, and exactly how it results in inexact copies of parents.
Further, every living thing on earth that has ever been found turns out to reproduce using DNA. Wow. That's a huge prediction fulfilled, just enormous. It's millions of predictions. If I read a story tomorrow that says that scientists have discovered giant worms in a cave in Brazil, bacteria in Antarctica, or a giant shark in the Mariana trench, I can predict they will reproduce using DNA, based on ToE.
That's just the fact that there is such a thing. It turns out that by decoding DNA we learn volumes about how organisms are related--more on that later. My point in this post is another huge prediction confirmed.