In one dimensional motion the initial instant of time or zero time (t = 0) is considered at the beginning of the observation of motion. It may not be the instant of beginning of motion. Suppose a ball is thrown from a height of 500 m. It becomes visible say at a height of 100 m. Then origin or initial instant of time or zero time (t = 0) is this instant only and not the instant when motion actually began.
Thus, if zero instant is considered as present then times before the instant is past and time after this instant is future