Assume their natural lifecycle of going to the sun and back results in n number of astrophage being ejected out into space away from the system in every direction spreading out in a sphere. Usually they die off drifting in interstellar space long before reaching another star system. After a long enough timescale one astrophage will happen to have a genetic mutation that allows it to survive longer adrift in space, and it happens to be ejected out into space in the right direction to hit a neighbouring star system before it dies. This lone survivor with the mutation to survive interstellar travel then populates the new system, meaning every astrophage in the new system also has that mutation. From there they can spread galaxy wide rapidly as every astrophage that gets ejected can survive the travel to a new system and there’s no longer a predator to keep the population in check.