Darwin believed one of the more popular explanations of his time: expanding Earth theory. Basically, the planet was like an expanding dough ball. It decently explained why things looked like they fit together. Darwin even went out to Patagonia to investigate some cliffs, and basically "confirmed" the theory.
So Darwin was trying to explain how creatures with common lineage appeared both sides of an ocean. He "proved" that the land masses were once joined. He didn't really care so much about "how" they were joined, but it was vital to his theory of evolution that they were.
Oh, definitely. It's also worth noting that he definitely wasn't a geologist, despite having an interest in it. I was mostly just mentioning it because there were theories trying to explain the similarities across landmasses before plate tectonics. We may not always be right about why, but we're really good at noticing stuff like that (even when it doesn't mean anything).
Deep time is so annoying. Here I am walking around thinking that I am the main event. And really I will be dead for decades in 1 855,000th of the amount of time from us to the dinosaurs. What the hell universe!? There shouldn't be 855,000 human lifespans between us and a bunch of overgrown lizards-bird things.