I have this vision of dinosaur astronauts, clinging to the rock that has been ejected into space, on their way to Mars to establish a new life there. I have always found the pan-spermia theories interesting. It still doesn't answer the 'where first' question but it allows for many places to share similar lifeforms without requiring a recreation of an improbable event in all of them. Of course it would be really weird…
... without requiring a recreation of an improbable event in all of them
Just to add to your post: the probability of such a spontaneous event (life emerging from a cocktail) increases as you're no longer looking at a restricted area. If panspermia is the mechanism then you don't require life to originate on a suitable planet in a Goldilocks zone. Every square mm of (often porous) rock flying around is a potential point of origin, carrier or seeding station.