That's not to say that we can now see everything we could eventually see, if we last long enough. Some galaxies that are just beyond our current horizon will eventually be visible; we can't see them now because (as far as we can see in our reference frame) they haven't formed, yet. We can in principle watch the process of star and galaxy formation in the early universe, as the universe evolves. As the universe expands, however, the recession velocity of the earliest observable universe increases, and time dilation dictates that it evolve ever more slowly, as the velocity asymptotically approaches the speed of light. That puts a strict outer limit on the matter we'll ever be able to see.