In 1977, ABC aired a television special titled The Making of Star Wars. This the first “Making of…” I am personally aware of, but was it the first ever such “Making of…” documentary?
It looks like The Making of Star Wars definitely helped popularize the "making of" documentary subgenre, since most of the ones I can find were made after 1977. There are several earlier documentaries about making films in general, or about the films of a specific director, like Directed by John Ford (1971), but very few about a specific film.
The earliest documentary I can find about a specific film is a short (28 minute) made for TV film about Stanley Kubrick's 2001: A Space Odyssey which aired in 1970.
Primer on the meaning, techniques and background of Stanley Kubrick's 1968 film "2001: A Space Odyssey." Keir Dullea, who starred in the film as astronaut Bowman, narrates on camera and over many excerpts from the film.
This may not be the oldest, but it only takes one to show that The Making of Star Wars wasn't the first, even if it is the earliest one that most people will remember.