You are correct. There's more to the universe than we can see, but what we can't see should be basically the same as what we can. By analogy, from any place on the earth, you can only see as far as the horizon[1]. If you were to teleport (or travel) to the edge of your horizon, you would see more earth that you couldn't see before, but that new stuff would basically be similar to the earth you're seeing now.
Just for kicks, let's add in that the earth is expanding like the universe. You're at point A, there's a tree at point B, and the horizon past the tree in that direction is point C. If the earth is expanding, then point B will be receding from both point A and point C, in part because point C is receding twice as fast.
[1] The reason for the boundary of the observable earth is totally different, but that doesn't change the point.
Just for kicks, let's add in that the earth is expanding like the universe. You're at point A, there's a tree at point B, and the horizon past the tree in that direction is point C. If the earth is expanding, then point B will be receding from both point A and point C, in part because point C is receding twice as fast.
[1] The reason for the boundary of the observable earth is totally different, but that doesn't change the point.