ratiocinator
Lightly seared on the reality grill.
..and how are you defining time?
What is a second? What is the frame of reference?
It is a model.
Without making definitions, we can't make a model.
It doesn't mean that our definitions are meaningful as to the actual nature of time through eternity.
One thing that we do know, is that measured time is relative to space in our universe.
One cannot come to meaningful conclusions about the nature of time as an absolute phenomena. It is a circular argument.
You define something, and then show it no longer exists at some point ? What doesn't exist?
The whole of the way science works and finds things out is by building models and then testing them to see if they match reality. If a model has been thoroughly tested and all of its predictions turn out to be true, then we can conclude that is a good representation of the world (at least within the scope of the model). When it comes to space, time, and gravity, we have a model called General Relativity, which has been thoroughly tested, and shown to be accurate.
That tells us that space, time, and gravity aren't actually separate things. Space-time is modelled as a four-dimensional manifold and gravity is the result of that manifold 'curving', that is, its geometry changes. Time is not the same for every observer. Even in 'flat' space-time, relative speed amounts to something like a rotation of what one observer thinks is the time direction through the manifold compared with the other (and likewise for what each thinks of as space).
We also know that space (that's space itself, not the things in it) is expanding, so if we extrapolate backwards far enough we get to a point at which the equations that describe space-time break down, and we cannot go back any further.
What actually happened at that point is not known because we know that general relativity does not take account of quantum effects, which we know will become important. However, we can't rule out a start of time because we know that it doesn't correspond to the fixed, eternal, never changing background that Newton described.