We're insignificant now. If we develop interstellar travel, we could start to become significant if we the visit/colonize the rest of the galaxy. Of course, even if we do fill up the galaxy, our galaxy is only a small sliver of the observable universe, so we'd have to move on to other galaxies. Not as crazy as it might sound, if given we would have the tech for interstellar travel, as intergalactic distances are only ~3 magnitudes off the span of a galaxy. e.g. Milky Way spans ~30k light years, Andromeda is ~3m light years away, 100 times. The leap from short hops of a couple light years to galaxy-wide distances is greater (Proxima Centauri is ~3 ly, vs. 30k light years = 5 orders of magnitude). Which is comparable to the jump from interplanetary to interstellar distances distances, which is about 4 orders of magnitude.

So if we can reach the edges of the Milky Way, other galaxies should be within reach. But doing that before the Heat Death/Big Rip/etc. might be a challenge.