I'm imagining two paths for life to spread between star systems. The first is via intelligent life actively exploring those systems—the purpose or mechanism of

I'm imagining two paths for life to spread between star systems. The first is via intelligent life actively exploring those systems—the purpose or mechanism of that exploration doesn't really matter; life could get there either way. So now you're comparing the statistical probability of abiogenesis against the product of the probabilities of a half dozen unlikely events (roughly, first abiogensis -> cells -> animals -> intelligence -> civilization -> technological civilization -> society stable enough to spread life amongst the stars). This isn't clear cut, but my best guess is that abiogenesis happening twice is rather more likely. The second is via some form of microbial life leaving the star system and spreading to other stars by accident (whether evolutionary accident or 'act of God'). I think it's possible life could leave the star system by some mechanism and with a ridiculous number of individuals and time could hit other star systems rather than floating in between systems forever. Then it has to land on a planet that not only doesn't kill it, but allows it to thrive. (Tardigrades aren't going to populate the moon.) I'm not sure how possible or likely this would be, but I'm guessing it requires a ton of time (that the universe may not have experienced yet) and, if it were likely, we'd have already found evidence of life on Mars.