early in the morning (Andrey Truhachev); in the early morning (Andrey Truhachev); as soon as day broke (Andrey Truhachev); at first light (Andrey Truhachev); in the early hours (Andrey Truhachev); in the early morning hours (Alex_Odeychuk)

idiom.

at sparrow fart (ВосьМой); at sparrow's fart (ВосьМой); at the crack of sparrow fart (ВосьМой); at the crack of sparrow's fart (ВосьМой); at all hours (Interex)

Makarow.

at an early hour

Schott.

in the wee hours (The event in question, which would soon become a full blown phenomenon, began in the wee hours of New Year's Day, 1970, and involved a group of Canadian nurses who would bear witness to a peculiar craft and a pair of bizarre beings that would forever alter the course of their lives.