Yep, you are 100% correct. In fact, it is much more likely they were originating on Earth itself than a random hobo asteroid.

> The missing part is how do they form self-replicating mechanisms capable of evolution.

Well, there are some missing parts, yes, but RNA can self-replicate already; at the least some RNA can. Ribosomes also contain RNA so its is a ribozyme.

RNA can replicate in highly artificial conditions that would seem to already require life to occur.