I, of course, have no definitive answer, but I am reminded of a famous quote, "Nothing is impossible, we just don't know how to do everything yet."
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Possible certainly, there's no known reason why it should be impossible, but it's plausibility is essentially unmeasurable without a fully formed theory of abiogenesis to base a judgment upon.You would be speculating in a vacuum, essentially.
Answer
Yes. Panspermia is the hypothesis that life arrived on Earth from outer space, perhaps amid, perhaps, comet debris.
There are ancient legends that comets passing over are associated with increases of disease. Can microorganisms survive in space and travel to Earth on a meteorite or comet? One of the astronauts apparently sneezed on part of the rocket apparatus in 1969 while prancing around on the moon. Bacteria from the sneeze survived all the way back to Earth in the vaccuum of space and survived the boilingness of re-entry through Earth's atmosphere. The bacteria from the 1969 moonsneeze were revived.
The hypothesis of Panspermia does not answer how life began or where life began but does answer
how life on Earth began. It is indeed plausible given the 1969 moonsneeze evidence. There are other ideas about origin of life on Earth itself such as the RNA world. The RNA world on another planet is also plausible, followed by meteoritic transport to Earth. Will we ever know which is utmostly correct?
A bit of correction to the above answer. When a technician was preparing a camera for one of the early unmanned moon landings he must have sneezed into the interior of the camera and then installed it on the spaceship, making no effort to sanitize the equipment. It was launched and stayed on the moon about 3 years. Then during one of the manned moon landings, an astronaut retrieved this camera essentially to see what 3 years of exposure to space had done to the unit. It was carried back to earth unopened inside the capsule which returned to earth and was not subjected to any of the reentry heat or pressures. When examined on earth it was found that the cold viruses that had been sneezed into the innards of the camera mechanism had survived the three years on the moon with no problems. They were intact and could have caused a cold to anyone handling those parts which were contaminated by the virus initially. This simply goes on to say that the potential for very small pieces of life causing DNA which is what viruses are, can survive the severity if space flight without much need for protection. Bacteria, which are true life forms, might not have been so lucky.
Other, more recent research, shows that although the outer surface temperatures of incoming meteorites is very hot for brief periods during the reentry flight the speed of these meteorites is not always as horrendous as most of us are of the opinion they are. One woman in Alabama in 1954 was laying on her couch when an 8.5 lbs 7 inch meteor crashed through her roof hit a radio and then bounced onto her hip. Although it caused a deep bruise, it was not so hot, or so fast as to have destroyed her hip on that left side. She went on to recover without much medical attention. This would imply that even bacteria carried inside such a rock might have been able to have survived the reentry too. The launch into space is conceived as happening when another small world not much different then earth or Mars where the initial impact sent debris flying at speeds faster then the escape velocity of that world. (25,000 MPH for earth). This would imply modest travel times from Mars to earth. but the reality is usually more like millions of years. Could this scenario imply panspermia? It is just not anything more then speculation with what we know today.