Some people say that time only began when the universe began. I think that is
At least movement is relatively clear, and in principle perceivable. But what is a "hypothetical or actual possibility of change"? (Are you distinguishing two different kinds of possibility here, one hypothetical, the other actual, or does this phrase somehow refer to one thing?) ... You'd need a rather thorough account of what "possibilities" are, in particular non-actual possibilities, to make this answer be an improvement on the earlier one .... (You might read Augustine's famous treatment of time, where he explores the relationship between time and motion: in his Confessions, ch. 11 .....)
hope that's a start!