Why can't we determine the center of the universe
There is no point of origin! It is a misconception that the universe started as a single point within space. Indeed, measurements since the 1990s seem to show that the universe is infinite in size, which means that the very early universe must have also been infinite.

It has not really been established that the universe originated from a "singularity" at all. We know that in the early universe everything was much closer together, and hence the universe was much denser. The "Big Bang Theory" goes back to the universe being extremely dense, but it is not required that the universe started from a single point.

Really, the Big Bang happened everywhere. Even at these early times it looks like it was infinite in size with basically constant density, and so there's no sensible way for it to have a centre.