This question is debated at length by those who are interested in the philosophy of time. The fact that so many philosophers of time can hold so many conflicting opinions about it (some of those opinions being at odds with physical fact) suggests that it is not one that is open to an easy or testable answer.
Some take the view that things (mass, energy etc) exist only in 'the present'. Another way of looking at that (which I favour) is to consider the present to be reality, and to consider time to be a counter which we use to keep track of change (I will explain that further below).
Others take the view that things continue to exist in the past, and some even think that things exist in the future.
You can describe the three views from a spacetime perspective by saying that the first view assumes that particles are points in spacetime, the trajectories of which are worldliness; the second group believes that particles are evolving sausages in spacetime, and the third group believe that there are predefined sausages stretching throughout time and for some reason we only see a thin slice of the sausage at any instant.
Applying Occam's razor, I take the view that views 2 and 3 are unnecessary elaborations. I also note that they lead to various types of paradox (which I might explain in an edited version of this answer if I get the chance).
Exocytosis asks 'If you move a mass in the x direction is it still in its original position when you have moved it?' That sums up my view of time. Those who argue for view 2 are effectively saying that not only is it still in its original position at the original time, but it is also in all of the intermediate positions at the intermediate times down to an infinite level of granularity. Thos who argue for view 3) are effectively adding to that by saying that the mass already was in all those other positions, and you just hadn't caught up with the fact.
I find it hard to accept views 2 and 3, and to consider them more positively I would need to be presented with a strong logical or experimental justification, neither of which I have been able to find.
If you accept that reality is what it currently is, time can be viewed just as a counter of how things change. Indeed the second is defined in just that way as a count of physical processes in a given type of atom. The concept of time as a counter of change automatically explains why time is one directional- if you count successive instances of things your count always increases. For example, if you count the transactions in your bank account, the tally inexorable rises in one direction. You must not confuse the count of the number of transactions with their cumulative value, which can go up or down or remain the same.