Hmmm, how could material processes occur in the absence of time? Serious question!
Heidegger more or less said we cannot understand Being, and you note he said time is an aspect of Being, so perhaps one could ask "why is there time rather than no time?" the same way we ask "why is there something rather than nothing?"
When I think of the absence of time, I think of a frozen world, include any thought of mine frozen as well. I don't think this is what Parmenides meant?
Kant and Selena ("wet savannah animals") are most on the mark from what I can see.