Andy Warhol’s film featuring a sleeping man is titled Sleep.
Sleep is an experimental underground film centered on poet John Giorno, who was Warhol’s lover at the time. The movie shows Giorno sleeping in black-and-white footage, using repeated shots and loops rather than a conventional plot. Its extreme stillness made it an early example of Warhol’s interest in duration, repetition, and anti-narrative filmmaking.
Although the question calls it a 1963 film, Sleep premiered in 1964 and is generally identified as a 1964 film. Warhol shot the footage during 1963, which likely explains the date confusion. The completed work runs 321 minutes, or five hours and 21 minutes, and was assembled from shorter pieces of film repeated over several reels.
Sleep was one of Warhol’s first major film experiments. He later extended the same fascination with prolonged observation in Empire, an eight-hour view of the Empire State Building. Kiss, another Warhol film, consists of people kissing, while Eat focuses on a man eating; neither features the sleeping subject.