I find this baffling. If we can observe objects moving away from us and each other, than it stands to reason that we can track their paths (relative to each other and ourselves) backward to find a point of origin. In this question answers given suggest that there is no center of the universe. I'm looking for clarification as to why we cannot reverse engineer (to some degree) where this point of origin exists, even if a simple general direction relative to us. I understand that paths may be distorted and skewed by forces as time goes on, but I still don't grasp the concept that we have no way to determine a point of origin or general sense thereof. Help wrapping my inferior brain around this is much appreciated.
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.