This is the theory of ‘panspermia’. The idea of living spores being blown between stars to spread life through the galaxy was first proposed back in 1908.

It has since become clear that unprotected microbes could never survive the harshness of space for long enough to be transported between stars, but there is rapidly growing evidence that cells can indeed survive the journey between planets in the solar system. Microbes could be ejected from their homeworld as stowaways within lumps of rock blasted off by a nearby impact, orbit through interplanetary space, and then make touch-down on another world falling as a meteorite. Experiments show that a proportion of cells can survive all the main hurdles of panspermia protected within their host meteorite: the heating and pressure-wave of being thrown off their planet; exposure to vacuum, freezing cold, and cosmic radiation whilst in transit through interplanetary space; and then the heat and shock of smacking into their destination. And it only takes a single bacterium to survive the voyage, to reawaken, grow, divide, spread beyond the impact crater to infect a virgin world, and subsequently evolve over billions of years into the vast diversity of organisms of a planet-spanning ecosystem.