I'm pretty sure Buddhist philosophy says consciousness is contingent with the senses and arises and passes away. The irony is, to know that, one must experience the arising and falling of consciousness. One example from the Satipatthana sutta: "Thus are formations; thus is the arising of formations; and thus is the disappearance of formations. Thus is consciousness;
thus is the arising of consciousness; and thus is the disappearance of consciousness." Naturally the irony of awareness of passing consciousness gives rise to lots of convolution as scholars continue producing knowledge to remain relevant.
There is no scientific rationale for consciousness apart from hypotheses that it emerges from activity of the brain (comes from material interactions). That aligns with Buddhist views on contingent consciousness. The difference is, Buddhists claim material and consciousness are concurrent whereas material science would assume material precedes the emergence of consciousness, but because experience isn't necessary for biological survival, there is no known reason as to why experience exists (see 'the hard problem'
https://www.youtube.com/watch?v=C5DfnIjZPGw). Hence, some scientists posit that consciousness is a fundamental property of space time (could be be measurable), but that's not science per-se as much as it is their personal philosophy.
How does this relate to time?
In the Buddhist view consciousness is not prior to or giving rise to phenomena. These are mutually contingent and occur concurrently. Hence, no time frame in which it endures is necessary. It's impermanent and momentary.
In the scientific view something has to be fundamental and prior to maintain some semblance of causation. Indeed most religious or any creation narratives must assume an uncaused causer like God. Of course, the causal paradigms require quite a linear aspect of time
I personally like how the Buddhists do away with a necessity for time, but not the facts that there are only so many hours in a day and each moment of life is precious.