[A Vast RightWing Conspirator]

Assuming the alien generation is as long as ours, this would take about 1200 years.

Of course, this makes zero sense, given that the Galaxy happens to be a few tens of thousand light-years across and that you would have to go 'around' the core to reach to the other side.

[Darth Reagan]

Apparently they aren't too concerned with travel time. Must have figured out how to open a wormhole/shortcut.

[js1138]

If you add 12 million years, 120 million years or even 1.2 billion years for travel time, you get the same result -- still a small fraction of the available time. If you postulate traveling at one percent the speed of light, and allow several centuries to colonize each new world, you still have time left over.

Perhaps not enough to colonize the entire galaxy, but certainly enough time to reach out several thousand light years.