It's a bit existential, but if you take the universe as we know it and subtract us from the equation, I will argue that yes, time will still exist. We do not need to be there to name it or perceive it any more than we have to see a circle for it to be round (even if we aren't there to call it a circle, it still exists.

Does MATH exist if we aren't there? Yes. sure we even if we arent there to figure it out, 1 + 1 will still equal 2.

The earth will still take a period to rotate, that's time
The light will still travel at a speed from point A to point B the measure in between? It's time

We can't shake it any more than we can make it.