I agree on that FQXi invited and hopefully will go on inviting new questions that may shutter tacit basic assumptions of science. Questioning the existence of time is certainly not new. Most winners of the first contest demonstrated their academic proficiency by efforts to defend space-time and denying some time notions of common sense.
If you ask whether or not something exists you mean is it something real, something actual. Mathematics shows that this is often a tricky and rather futile question. Does the square root of a negative number exist? Obviously not, unless one allows for imaginary numbers.
I feel ignored because I consider the usual, so called scientific notion of event-related time insufficient as soon as one considers how something exists in reality. Common sense has it: There is a complemenrary notion: elapsed time.
Einstein is often quoted having said: "Time is what the clock reads". Nobody can read future time. Any clock shows always only past time.
Eckard