Large meteorites have hit the earth, creating a splash, launching chunks of earth into space. Many of those chunks probably had living microorganisms which hitched a ride to whichever next planet that launched chunk of earth then smashed into.
Inspired by Martian meteorites that landed on Earth.
In this way, Earth has probably seeded a large, perhaps cone-shaped, region of the galaxy (or beyond) with life over that past 3 billion years. Maybe like a contagious constantly traveling constantly sneezing patient zero. How large is that region?
If there is a habitable planet within that region, what is the probability it escaped infection by Earth? On one hand, space is big. On the other hand, there has been a lot of time. There could also be indirect infections where a planet seeded by Earth thrived, got hit by another meteorite, then chunks of it and its life get launched into space (propagated outbreak in epidemiology).
Of course, one wonders whether Earth itself got seeded from elsewhere.