The above comment is the best answer because it focuses on your primary misunderstanding which is that the past we are seeing into is not the past of “our part” of the universe.

The universe is likely infinite. The observable universe is a sphere with us in the middle. The edge of the sphere is where we see the oldest parts of the universe because the light from these distant places is just now reaching us, showing us what things looked like back then.

This sphere is getting bigger for an obvious reason, more and more light from distant places is reaching us. However, the sphere is also getting bigger because the entire universe (not just the observable universe sphere) is expanding.

Careful here not to imagine the entire universe’s expansion as a sphere, but rather every galaxy that isn’t locally bound to another galaxy by gravity is moving away from one another.

An oversimplified way to imagine this is to visualize an infinite 3D space with tennis balls each 10 meters from one another in every direction. Move forward through time and as the universe expands they are now 20 meters away from one another. Move back in time and they are 5 meters away from one another and so on.

The interesting thing is that, though the speed of light is constant, this expansion of the entire universe seems to happen faster with the more space that there is between things, as if the space itself was causing the expansion (we call this mysterious force Dark Energy).

What this means is that eventually the expansion of the entire universe will outpace the speed of light, making galaxies we can currently see in the observable universe fade out of sight as they slip out of our observable universe. Eventually, only our own galaxy (at this point merged with Andromeda) will visible to us, everything else too far away and the universe expanding too fast for new light to reach us.

If humans still exist in this time, they would have no knowledge of other galaxies and the universe unless we managed to pass down the data from our time.