In a human with normal sleep architecture, sleep cycles occur in roughly 90 minute bits. During a cycle, our brain cycles through different stages of sleep, from light to deepest. Stage 1 -> Stage 2 -> Stage 3 (Non-REM sleep) and then finally Stage 4 (REM sleep), then starting a new cycle we revert back to Stage 1.
The average human will be doing about 5 sleep cycles or so a night. For the first few cycles, there isn't too much REM. There can be a couple minutes or so of REM at the end of the first two-ish sleep cycles.
As the night goes on, especially towards the early morning, the latter sleep cycles contain proportionally more REM sleep compared to lighter sleep than earlier cycles. It is during these last sleep cycles that we get the bulk of our REM.
However, if one is sleep deprived, REM sleep rebound can prove powerful, causing earlier sleep cycles to contain more REM than is usual. Or if one falls into REM while part of the brain is still awake, sleep paralysis
While there are alternate sleeping cycles that some have used, I think we still need ~6-8 hours of full cycles following a normal circadian rhythm to be at our best. There is a sleep method (I can't remember the name of) that involved sleep depriving one's self to the point where REM sleep rebound is very strong, and then training one's self to sleep during the day in small increments, essentially a bunch of REM sleep naps.
The idea of that technique was to enter into REM sleep very quickly, but this method seemed to sacrifice much of the other stages of sleep which are still beneficial for the brain, but particularly beneficial for the body. The majority of e.g. growth hormone release occurs during slow wave sleep/non-REM sleep.