When events due to accelerating (changing) force fields occur, there is always an order of movement in densities of fields - superposition and relative displacements in general are different. Yes, time does always exist when there is anything to measure rate of relative change in internal and external systems, I would intuitively postulate.
If even the smallest sub-atomic particle makes a movement, like even a wobble, it has changed position, a change in position is displacement and displacement requires a time component.
The only way Time could not exist is if nothing at all in space, even before our universe formed, there had to be no motion of anything, even the event of a Creator thinking about creating the universe would require a time component.
There is also the possibility that the Big Bang occurred when two Black Holes (remnants of previous universes) Collided. There could be no Collision without displacement and thus Time Existed.
Regardless of your world view, Time had to have existed prior to the Big Bang, yet, it was a different time model to that which we know, since there were no planetary motion nor stars to derive any regularity or sequence from. So, days, weeks, years did not exist. Only movement of a couple or more black holes, drawing the other black hole in.
So, time as we know it did not exist, but, there was always an element of time, since, without time, there would be no movement nor thoughts from a creator, as all require a time element.
Even a single Higgs-Boson particle or a dark matter particle/cloud moving through space would create a time instance.
A thought even requires time to produce!
The only other place where time may not seem to occur is in the center of a Black Hole.
Though, on the surface, it is a different matter, as time certainly exists there with particle movement as matter is drawn in.
I'm no physicist or reader of the bible, but my gut reaction is that time existed prior to our universe. Time is a concept, not a concrete thing. Even if there was no one there to see it or nothing to move around, moments still happened in a particular order.
There was no time before the big bang and... Possibly... The universe before this one. There was no TIME itself. Time was created with the big bang. That's pretty much it. (Unknown really, but that's my theory, because how could there be matter... But no time? Or time... But no matter?)
Time is a means by which people, and scientists, measure events. Time is a man-made tool that measures periods, whether it be movement, physical change, or anything else scientists wish to study.
Did "time" exist before the universe - Yes technically - because anything that is wanted to be measured can be measured. To use a rudimentary example, "time" in the layman's terms, is measured on a clock between numbers. Before that, Time was measured by noticing the change of shadows from one place to another, and before that time was measured merely by the rising and setting of the sun, or the change of seasons, or the growing, blossoming, and withering of a plant.
So, if someone wishes to measure the universe, determine a create date or any other measurement that would identify a beginning or end, that person is USING time to complete the measurement.
I think the concept of TIME is being used in the wrong way.
We have this prevailing notion that time allows motion: however, using the dimensional theory of the universe (that time in a three-dimensional universe is just the passage of four-dimensional objects through three-dimensional space) rewrites this causation: time is allowed because of motion. Thus, because a quantum singularity (before the universe) can have neither dimension nor motion, it cannot create time.