No, you have it wrong. It's not that everywhere is (rather can be) the center means that every point is the the same point.
Think of longitude on our planet, any particular point excepting the poles [which define the latitude] could be our 0 degrees [the prime meridian] as it is arbitrarily chosen; this does not mean that every point on the planet is the same.
(From Wikipedia)
By convention, one of these, the Prime Meridian, which passes through the Royal Observatory, Greenwich, England, establishes the position of zero degrees longitude.
[...]
Note that the longitude is singular at the Poles and calculations that are sufficiently accurate for other positions, may be inaccurate at or near the Poles. Also the discontinuity at the ±180° meridian must be handled with care in calculations. An example is a calculation of east displacement by subtracting two longitudes, which gives the wrong answer if the two positions are on either side of this meridian.
But it may actually be true that every particular point is the center of the universe. Consider the big bang, if at the beginning of time [t=infinitesimal] the universe was a single point then any point in today's universe is derived from that point thereby making all points the center.
Change, put in simpler words, is simply impossible without the lapse of Time.
You have it exactly backwards: time is the measurement of change; that is time is dependent on change... not change dependent on time.
With the longitude example, you commit the error of mixing up axes and spatial position. The longitude fixes the rotational position about the axis of the Earth, from an arbitrarily chosen reference. The value of that rotational position is constant between the poles along the parallel (coplanar) to the axis of the Earth because you have not changed your rotational position which the longitude defines. This is nowhere applicable as an analogy to the actual point we are discussing - which is picking a moment to begin something, when you don’t have Time as a fundamental dimension to define that beginning moment.
If the Universe was a pinpoint of say 1/1000th cubic inches spherical volume, what was present to define the boundary of this pinpoint radially away from the centre? More space? A mirror?
Are you saying that if nothing changes, Time stops? If so, when exactly does Time start to flow?