The big bang may have two different meanings:
First, a phase of very strong inflation of the early universe. In this sense the big bang is widely acknowledged.
But we have very little ideas about what was happening before this inflation phase as it seems that the known laws of physics cannot be applied. There are two main possibilities: Initially the universe may have been very small (condensed) or it may actually have been pointlike (point, planck volume or similar).
Also, you have to distinguish between space, spacetime and time. Spacetime is a relative and observer-dependent notion. It is a mechanism which is conjugating space and time. Time in an objective, Lorentz-invariant sense is the proper time, the duration of a mass particle. Spacetime is telling us if two particles which are travelling through the same point in space are doing this simultaneously (causing an event) or not.
By consequence, time is a fourth dimension only within the limits of spacetime. There is no other similarity between 3D space and time which is just duration of particles. Every observer perceives 4D spacetime, but simultaneity is only a relative concept. There is no objective 4th time dimension.
By consequence, the answer to your title question may be: yes, initially spacetime coordinates of our universe were strongly reduced, perhaps even pointlike.
But it would not be meaningful to call it a temporal center: As I pointed out, time is not a fourth dimension, but only duration of particles. And even within spacetime (where time may be considered as a sort of fourth dimension) this does not seem to make any sense because spacetime is relative and observer-dependent, and it is not "analogous" to space. Every particle developed differently since the big bang (example: fast moving electrons aged less since the beginning of the universe than comoving reference frames)
If we consider the BB to be the Beginning of of our universe, can we
call this the Origin of all of the 3 dimensions of space and the 1
dimension of time?
The beginning of spacetime: If we suppose that there was a pointlike big bang, we can say that this was the beginning of spacetime. However, there might have existed some causality which produced the big bang. There may have existed (a) spacetime or something else before the big bang.
The beginning of time: The answer is similar to the answer about spacetime. Time in an absolute sense is proper time and duration, as far as we know only mass particles have a proper time.
The beginning of space: It is currently supposed that inflation (even in the sense of inflation of a pointlike big bang) does not happen into something but that space itself expanded. That would mean that the answer would be similar to spacetime and time.
And so my point is this: what are we doing when we look way out in
space? Looking back in time.
We see the universe as it was in the past, that is right. But when we are looking out in space, that means that photons reach our eyes which have travelled for billions of years. A photon coming from another galaxy one million light years away has travelled one million years. By consequence, these are photons of our present time, not of our past.