Once we can see them, it’s too late
This kind of assumes that a “maxed out” civilization can expand at speed of light, but I don’t think it is given. It may very well be that meaningfully massive transport cannot exceed even a small fraction of <i>c</i>. After all, propulsion has to make energetic sense.<p>1. There is energy to get to speed<p>2. Mass of fuel to decelerate (and you have to accelerate that fuel in the beginning!)<p>3. Highly blue shifted CMB (that alone limits how close to c you can get before becoming plasma)<p>4. Collision with micrometeorites (so the “ship” has to be microscopic or probability of collision quickly goes to 1, and there is no way to survive even micro collisions while moving at c).<p>5. Limits on how fast you can give impulse (because your ship is made of matter with finite strength). Eg You cant reasonably railgun something to close to c without converting it to plasma.<p>There is also all the things you do when you get somewhere before sending more probes to expand, presumably it’s not a single location that seeds everything else (and if it is then the energy budget of that is also complicated).<p>Now, even at 0.1 <i>c</i> and with many pauses to replicate on the new worlds it would still take only a few million years to span the milky way, but if someone was mid-expansion we would see them way before the bubble hits. Being limited to 0.1c also means that those not in our galaxy will likely be unable to expand into ours (and vice versa).