The assumption that time does exist, which is physically distinct from spatial dimensions and exists independent of measuring properties of objects allows the prediction & explanation of a wide range of phenomenon that otherwise cannot be explained.
To exist is to occupy a region of space for a duration of time. Time by the reflexive property occupies all times, so if time is present in any spaces at all, then it exists. And time does exist in my room.
Definition of exist: Dictionary.
Presence of time in my room: My clock.