From a scientific point of view, sleep happens in stages: drowsiness (where you’re still aware of your surroundings); disassociation (where hypnagogic visions occur); and dream-consciousness (where the individual is in a state of self-consciousness but with every day parameters altered per the dreamer). Falling asleep is not unlike a windmill turning, where the contents spin in the person’s consciousness while the person sleeps.
According to the America Heritage Dictionary of Idioms, the literal usage, which uses the verb fall in the sense of “succumb,” dates from to the 14th century. However, in the Annals of Ulster covering 431 through to 1540, it documents the falling asleep of the son of the Carpenter, Ciaran, in the 34th year of his age, or in the 7th year after he had commenced to build Clonmacnoise, Tigernach of Cluain-eois died.
From this, it is understood that falling meant passing suddenly from one state to another as in going from being awake to being asleep or being dead.
On August 15 of every year — and dating back to the 4th century — the Catholic, Eastern Orthodox and Eastern Catholic churches (the Scottish Episcopal Church and the Anglican Church joined in this celebration in later centuries) celebrate the Falling Asleep of the Virgin Mary. So the phrase “falling asleep” dates back at least to the 4th century and possibly reaches back even further.