The typical way to picture the universe is like the surface of an expanding balloon, a 2-manifold which happens to be embedded in 3-space. If you picture galaxies as spots on the balloon, there's no "last" galaxy, they're all roughly equidistant from their neighbors. Analogously, our Euclidean universe is thought of (in terms of noncompact spatial dimensions) as an expanding 3-manifold. There's no last galaxy there either. However, if you include time, then at some point in the distant future there will be a last galaxy because old stars will all burn out or be sucked into black holes. And further in the future protons will decay, so there will be no baryonic matter left, plus black holes will eventually evaporate. Much sooner than that though, the continued expansion of spacetime means that galaxies will in time disappear over the expanding cosmological horizon, and future lifeforms will know nothing of the universe outside their own aging galaxies. See: https://en.wikipedia.org/wiki/Future_of_an_expanding_univers...

The last thing we can see with light in any direction is the background radiation. That's when light and matter separated.

That's why gravitational waves are such a big deal: they allow us to look further. (Not further than the limit imposed by the speed of light, though.)

I think they would have to be at the edge of their galaxy for this effect to take place ..

Obviously I have no evidence, but my suspicions are that its like the pac-man world, it just continuously loops on itself. Its just really big...

Too late to edit, but I must add that I'm not necessarily asking if there's an "edge" of the Universe.

I don't see how our situation is any less terrifying haha