The past does not exist, and the future has yet to be. There is only the immediate present. However…
You can never pick out an instant in time. If you do, I would ask “Where is the next instant”? You could never point to it, because given two instants in time, and thus, two points on the number line called the timeline, there are an uncountably infinite number of points between the two first instants.
Thus, in a sense, there is no “dt” of time, as you would assume in calculus, but rather a “delta t,” some infinitesimal, non-zero length of time.
Where does this come from? From the very nature of spacetime and the Special Theory of Relativity. Every particle, bit of energy, photon, location in space, has its own “clock.” Given that spacetime is smooth and continuous, what links together all of these clocks is that fact that everything has to get to the point in spacetime that it is supposed to be at. This is where you get a “delta t” of time, and that there cannot be an “instant” in or of time.
Psychologically, we have “the immediate present,” which psychologists tell us “lasts” about 3 seconds. But it’s a combination of memory and the brain projecting forward expectations of how the immediate world is supposed to be.
Given our memories of what happened, we have this crazy concern as to why time’s “arrow” always appears to point “forward.” The fact of the matter is that with regards to time there really is no backwards or forwards, rather, things happen as the laws of physics and causality demand. Every particle and bit of energy is heading to its next position in spacetime, and, given that we have memories and that our brains project the future (or rather our expectation of it), we get this crazy idea/concern as to why time only moves “forward.” It’s not time that has the arrow. Rather, everything is headed to where it’s supposed to be next. There is no arrow to time.