There are meteorites on Earth which very likely originated from Mars. They're believed to have been launched into space by an impact, eventually finding their way onto Earth. If we're looking for the most realistic options for panspermia to have occurred, they'd be due to a natural event of this sort.
It’s very much like how islands in the sea are colonized by life. Some event causes a blob of living creatures to enter the sea on a raft and they drift until they make landfall somewhere else. Sometimes they survive long enough in the new place to reproduce.
Rats leaping from a sinking ship swimming to shore we were.