Galileo claimed that tastes, smells, colors and so on, reside in consciousness. Hence - if the living creatures disappear, all these qualities will disappear. "
In the same way time is a parameter of consciousness which is perceived when there is movement.
Movement exists when I have a will that I have not yet achieved so I often move in order to achieve it.
Conclusion: If an infinity of filling would have fulfilled my will until it left not a single drop of disadvantage in it, in such a situation there would have been no need for movement and hence the time would not have existed.