the.com/ungodly hour

means An hour so early (or late) that it feels unreasonable to be awake or doing anything during it.

from From "ungodly," literally meaning irreligious or sinful, which by the 17th century had broadened into a general term of disapproval — "ungodly" came to mean simply outrageous or unreasonable. The pairing with "hour" leans on the old idea that pious folk kept respectable hours, rising and sleeping by the sun, so any hour outside those bounds was, well, godless. The phrase has been a humorous complaint about absurdly early mornings for a couple of centuries.