This. Not all ejecta from asteroid/comet impact is vaporized. Some is launched at escape velocity mostly undisturbed[1]. Mars both cooled first, giving it a leg up to allow biogenesis[2], and has lower escape velocity, making easier for rock chunks to be launched from there to Earth, rather than the reverse. From thousands of impacts and billions of rock chunks ejected from Mars in the early solar system, the successful delivery of a single viable microbe would be enough to seed Earth.

[1] https://fire.biol.wwu.edu/cmoyer/zztemp_fire/biol345_F10/pap...

[2] https://arxiv.org/pdf/astro-ph/0403049

>Some is launched at escape velocity mostly undisturbed[1].

Does that mean there could be bit's of actual dinosaurs floating out in space?

I didn't think of it that way around. So maybe we are all Martians really.