Earlier quoted context omitted.
Not sure why it was downvoted. Many people have looked into this. https://gtocx.jpl.nasa.gov/gtocx/competition/ Even entire competitions to find optimal colonization methods. Could take 90M years with measly future human tech. Age of Milky Way is 13.5 Billion so even conservatively you could indeed colonize the galaxy many many times over in that time.
The Milky Way lacked rocky planets early on, making that 12.5 Billion year age largely meaningless. Which is just one of many bad assumptions in how people do these calculations. At a minimum you don’t get a straight path from A to B. Assuming any kind of limitation in distance traveled and your at the mercy of the distribution of whatever resource you need. Aka need rocky planets with liquid water, that’s likely goi…
This doesn't seem like a good idea if their method of traveling is generation ships. What would be the point?