How Can Anything Exist?

Sorry to harp on about this, but the essence of my last post is bugging me mercilessly. The logical mind entertains the simple view that all events have three stages:

The unformed possibility – the future – the prospect. At this point we say they haven’t happened yet, and they won’t exist until they do.

The historical event - the past – the memory. At this point we say they happened once, but they’re gone now. They no longer exist.

The now. We think of this as the current, actually existing stage. But time never stops flowing, so there never is an identifiable ‘now.’ However much we subdivide time, ‘now’ is the bit that can’t be subdivided because anything that can be subdivided must, by definition, have a start and end point. ‘Now’ is the bit in the middle, which is a contradiction in terms. There is no middle.

So, on that basis, every event goes from being something that doesn’t exist yet, to something that no longer exists, and passes through a non-existent point on the way.

How does this square with our perception of reality? What am I missing?