In nerdspeak, the geometries are not the same, one is isotropic the other anisotropic
The universe is expanding faster than the speed of light beyond a distance of 13.7b ly away, and the comoving diameter of the universe is already something like 93b ly. If you could teleport to another part of the universe, you would have a whole new local environment, but it would still be flying apart faster than you could ever hope to catch up to the furthest objects (without another teleport), and the furthest objects you can reach are getting more and more sparse as they are always flying outside of your observable universe. I.e., inside a black hole, where all possible directions only point further inward, and yet also "away from everything else", as anything that fell in before you, gets pulled in faster and faster "away from you, towards the singularity", and anything that falls in after you has increasingly no hope of catching up to you.
Time doesn’t seem to end in the universe at large…
we're going to end up in one of those super-large black holes in like 20 or 50 billions of years. One can say that we're already falling into that blackhole. And the geodesics of our local Universe end in the core of that super blackhole. The core of that blackhole can be considered the center of our local Universe the same way like the core of any blackhole is considered the center for everything falling into the blackhole.
This idea could have legs if the math works.