Centerless expansion or a matter of perspective
The first principle of cosmology is called the "cosmological principle", which asserts that the universe is more or less the same everywhere spatially, but changes with time.  This is a fundamentally new way to think of the history of the universe, and has revolutionized our ability to understand long-range observations.  We do not, however, know that this principle is true, we only know it is both useful and consistent with all observations.  So we adopt it as a working hypothesis, and all of cosmology follows.  Some day we may discover it is inadequate, but until then, we will continue to use it.  The same could be said for other principles, like conservation of energy-- we don't know that's true either, but it's useful and consistent with observations.  The cosmological principle rules out that the universe has a unique center.

Your question is whether the apparent lack of a unique center stems from our location not being special enough to be able to tell that it does have such a center (say, by encountering a boundary).  Ironically, the cosmological principle turns that question on its ear, and points to the possibility that one's perspective always puts themselves at the apparent center.  So we would say the illusion of having a center is all about perspective-- not the illusion of not having a center!