Buddhist philosophy of anatta challenges the notion of "entities" - objects with identity, independent of the rest of the world and observer.
Instead, here is an alternative: try and see the world as a connected network of causation, with a system of nominal entities overlaid on top. In other words, consider that entity is a construct of the mind. (This simplifies things a bit, as the network of causation is a concept as well, and even the mind itself is dependently co-determined by its objects - for those Madhyamaka nitpickers - but stay with me). What's important is to understand that the real world is not discrete. Discreteness is mind-made.
If we extend this from spatial to temporal relationships, we can see that event is a temporal counterpart of an entity. Indeed, event is something that has a definite identity, beginning, life span, and end. Exactly like an object. In our mind event is separated from its context, from the rest of the stuff going on before, in parallel with, and after.
But in actuality, that's never the case. Objects and events don't exist by themselves. At first approximation we can say they arise from causes and conditions - so when those conditions and causes come together, thereby is an object or event. And when some of those conditions and causes fall apart (the necessary ones) - the object or event is no longer.
If we look more carefully though, we will notice that causes and conditions don't live in isolation either - they are infinitely forking and joining, infinitely interacting. So it is the mind that picks a subset of causes and conditions to focus on and label; the mind assembles an object that would satisfy mind's predispositions. Similarly, the mind assembles an event, assigns it with identity, and cognizes its beginning, span, and ending.
So it's not that events don't exist because everything lasts only an instant. Events don't exist because they are discrete constructs, overlaid on the (analogue?) fabric of reality.
The experience of any (assembled!) entity or event is necessarily subject to beginning and ending, subject to impermanence. Because an assembled object cannot exist once its constituents fall apart. What you call "now" is itself an assembled entity. It depends on a number of conditions coming together in a certain way. When those conditions following their natural courses fall apart, that particular "now" is no longer, and a new "now" is assembled.
Because we ourselves delineate the entities/events, we can choose the level of granularity to apply. We can designate big objects (systems of components) and big events (massive events) - or we can observe at the small scale. (Check out "Hierarchy Theory" by Valerie Ahl for a modern treatment of this thought.) So is with observation of present, it is up to us to decide when the given present has begun and when it has ended. Ground reality is analogue, not discrete. (Technically speaking, both analogue and discrete are two sides of the same coin, two truths are really one and the same truth.) "Now" is not instantaneous nor an interval. It's a nominal designation.
All experienced phenomena are mere products of conceptualization, merely nominal entities without any ultimate existence. Therefore sentient existence necessarily involves suffering that comes from mismatch between the concept and reality.
The mistake we make by default is to assume that experienced reality is made of stable entities. Then we build expectations around this assumption, and then we suffer. So once we know the trick, we can see through it. But because the nature of mind is to fabricate experience, it keeps doing it whether we want it or not. Not just fabricate, but use these fabrications as foundations for its interpretation and decision-making activity. There is simply no other way to operate. So all our experience and behavior is necessarily based on layers upon layers of fabricated quasi-stable virtual structures. Which means suffering will inevitably sneak in here and there. But at least now we can include the above in our working model of reality, and account for the non-substantiality in our interpretation and decision-making activity. So even when we have to walk on illusions, we know what we are doing, and are ready to deal with it once they collapse. It may still be painful when it happens, but we will have expected it, and will minimize the damage as much as we can. This is the extent to which there is an escape from suffering.