Time must exist for non-existence to lead to consciousness. If one removes time as fundamental and makes it emergent, that also removes agency.
From the frame of the perceiver, the absence of perception is the absence of everything. It does not matter that the universe goes on without consciousness, or not. For the conscious perceiver, there is no passage of time, when consciousness ceases to perceive.
Considering that I am unaware of my state of being at the "Big Bang" (The beginning of the Universe, and the start of that first quantifiable moment), I can only know about the existence of time before me through a constructed/reconstructed model (i.e.: mathematics). My understanding of the vastness of the time since that first moment, tells me it is actually very quantifiable, even falsifiable, depending on our definition of the "beginning".
Logic tells me that that couldn't actually be the beginning of something so enormous, something so vast, so incomprehensible, as All Existence, so our mathematics is inadequate or our definitions, based upon some concept of the infinite, is misleading.
In all cases, the actual time in which existence has been, is just a flash, maybe not without dimension, but from a relative perspective, it can't be nearly so large as non-existence, except that non-existence is dimensionless.
For reincarnation, who to say that each incarnation of a life is time sequential, or even within the same universal framework?
Of those who believe in reincarnation, only a tiny handful claim to remember their past lives. Maybe they are right, but that only suggests that everyone has experienced a past life that happened in the past. Maybe, for most of us, our past existence has been in the future, another present loci, or in another universe completely; which could explain why we don't remember our past lives. The loss of sequence renders our memories null.
-Will