It might be helpful to think in terms of the respective movement of points on the surface of an enlarging sphere, (like a balloon being inflated from within) -
As the sphere expands, any two points will move away from each other faster in proportion to there distance at any given time.
There is no preferred point of reference from which to measure the expansion of a sphere other than the point you happen to be measuring from. From any other point on the sphere you would observe a similar rate of expansion.
The expansion of the universe appears to be much like the sphere except that the expansion is not confined to the surface of our imaginary sphere but extends in all directions, like a rising lump of dough without a defined surface or center.
When we look at the most distant observable parts of the universe all around us, ~13.6 billion light years away, what we see is what was there back when the universe first became transparent. If you were to be transported instantly to the most distant point in the universe from where we happen to be in it, it would appear much the same as it does here, stars, galaxies etc. only from there we would see it as it is now ~13.6 billion years later.
Although when we look out we are also looking back in time, towards the beginning, the past we see is merely an allusion of time due to the time it takes light to reach us. We see it as it was, but in reality, the entire universe is all the same age.