Mars is smaller and cooled down before Earth. That means it had liquid water while the Earth was still too hot. Therefore, it's possible that life first appeared on Mars, and was later transferred to Earth on a meteorite.
Interesting. How would a meteorite pick something up in one planet to carry it to another planet? I'm presuming that the hypothetical meteorite does not originate in Mars.
A big enough meteorite impacts Mars hard enough to blow up bits of the latter beyond escape velocity, those bits then float in space for a long while then some may end up being captured in Earth's gravity well all the while evading Moon's one, and if big enough maybe becoming meteorites themselves over here.
It's kind of a mind boggingly huge billiard game.
With a bit of luck, life was somewhere around the initial impact, a couple bits of life survive blast energy, cold of space, radiation exposure, passage of time, atmosphere entry, and impact, and finally feel cozy enough on the new rock to replicate.
Now, the metagame is to assign numbers to all of that, and compare that to the odds of molecules assembling themselves into spawning life locally by itself. Also the latter must have happened somewhere first anyway, the question mostly being which of it is it for Earth.
This seems incredibly far fetched but the time scales are galactic, and so it kind of looks like it happened a few times over but we're not quite sure yet:
