Assuming that there is a volume in universe where light havent reached yet from the beginning of the universe and every matter(or anything) is so far away from that it so no field from that even reached there yet so if we have to discuss about the presence of time there how can we say that time is also there yet...means how we can relate time to pure space(entirely empty space)? How to prove that time is there?
The perception of the passage of time is the increasing in entropy of the system. If your "supposedly volume of the universe does not change as it reaches maximum entropy, then there is no way to measure the passage of time. Therefore, time stands still.