That raises another interesting question: how quickly could life-bearing ejecta from Earth (or anywhere else) seed the entire galaxy?
Hara and co calculate that it would take some 10^12 years for ejecta to spread through a volume of space the size of the Milky Way. But since our galaxy is only 10^10 years old, a single ejection event could not have done the trick.
However, they say that if life evolved at 25 different sites in the galaxy 10^10 years ago, then the combined ejecta from these places would now fill the Milky Way.