You aren't being very consistent your proton which you are happy to say exists can only be defined by a wave.
I am never happy to say that anything exists. If I make such a statement you can generally assume that it is “shorthand” for something like “We detect what we interpret as its physical existence”.
So if your proton can only be described by a wave then time must exist for the wave to exist
As you say: it can only be described by a wave. This does not guarantee that it is a wave. My understanding is that quantum objects are neither particles nor waves.
(wave = movement in time BY DEFINITION).
Even disregarding any doubt that the proton might actually be a wave; all this establishes is that change takes place; time might only be the tool we use to make sense of what we call change.
