The idea of a chunk of Earth containing the first bacteria being blown into space and reaching another galaxy is highly unlikely. While it's possible for debris from Earth to escape its gravitational pull and be propelled into space due to an asteroid collision or other catastrophic event, the chances of it reaching another galaxy are incredibly remote for several reasons:
Vast distances: The distance between galaxies is immense. Even at the speed of light, it would take an incredibly long time to reach another galaxy. The closest galaxy to the Milky Way, Andromeda, is about 2.537 million light-years away. Traveling to another galaxy within a human lifespan or even over billions of years is currently beyond our technological capabilities.
Survival in space: The journey through space is harsh and inhospitable. Extreme temperatures, radiation, and the lack of a protective environment would make it extremely challenging for any form of life, including bacteria, to survive such an intergalactic voyage.
Evolutionary timescales: Even if a chunk of Earth did manage to reach another galaxy, the timescales involved in the evolution of life are vast. Evolution typically occurs over millions or billions of years, and the conditions and environments in a different galaxy may differ significantly from those on Earth, making it unlikely that Earth's bacteria, if they did survive, would evolve into something drastically different.
While the concept of panspermia suggests that life's building blocks or even microorganisms could be transported between planets or even star systems, the chances of intergalactic panspermia are highly speculative and currently lack substantial scientific evidence.
In summary, the scenario you described is highly improbable due to the immense distances involved, the hostile conditions of space, and the vast timescales required for evolution to occur.