In the absence of time, events cannot occur.
Or to put it another way, space and time do not pre-exist, they are created as the universe expands.
If you believe that wave mechanics is at the root, then you must also have some explanation for the origin of inertia, space and time - and of course, physical causality.
The scene of the Dodo birds in the animated film "Ice Age" comes to mind. It was hilarious, the point of the scene being that they were too stupid to survive.
If you say so. Is the universe expanding? Does time and space depend on an expanding universe? I don't know.
What is is. If we are waves, and selection events like asteroids or gamma ray bursts are waves too, then evolution reduces to destructive or constructive interference between waveforms. Reality becomes the inevitable consequence of an initial asymetry in the birth or rebirth of the universe. We are then simply the result of anti-entropic local forces in a universal sea of entropy.