Not really. Existence without change is still existing. Change cannot occur without an existence to change.
Existance need time to change.
Existance cannot change without time.

Oh, so you admit it's a crappy explanation. And it is. Especially since it is in all ways functionally identical to time compression, except that you insist it goes on forever and that Ultimecia's two forms do something different than their scan info states.
That is not crappy explanation but that is simple explanation about New Dimension of Time.

By the by, I realize you keep trying to use the term 'dimension' equivocally. I suggest you don't. For one, it makes your already fuddled argument worse, and for two, it's bad debating.
Using dimension term is the best way to explain time.

If space/time came into existence with Big Bang, how could the cosmos be of infinite volume?

It appears that universe is either infinite, containing an infinite number of finite systems, or, it is finite, containing a finite number of infinite systems...which seems much more difficult to grasp than infinity itself.

The universe is only finite in its infinite capacities