When Does the Film "October Sky" (1999) Take Place?
"October Sky" is a historical fiction film written by Lewis Colick [adapting "Rocket Boys" (1998) by Homer Hickam Jr.] that released February 19th, 1999. So when is "October Sky" set?
It takes place in the years:
We know this because when Homer Hickam travels to Indianapolis, Indiana for the National Science Fair he sees a movie theater with "The Incredible Shrinking Man" on its marquee and the film "The Incredible Shrinking Man" (1957) debuted in theaters in April of 1957 AD. So it must be during or after April of 1957 AD.

1957 AD - 1958? AD
We know this because when Homer Hickam travels to Indianapolis, Indiana for the National Science Fair he sees a movie theater with "The Incredible Shrinking Man" on its marquee and the film "The Incredible Shrinking Man" (1957) debuted in theaters in April of 1957 AD. So it must be during or after April of 1957 AD.
More specifically, very early on Homer and his class are discussing the recent launch of the Russian man-made satellite Sputnik I, which launched on October 4th, 1957 AD but was not noticed by Americans until October 6th, 1957 AD in the real world. So it is early October of 1957 AD at the start of the story.
Also, the movie begins with radio broadcast about Sputnik I's launch and includes the phrase: "If you have just tuned-in to this special bulletin, Washington has confirmed that yesterday, on the 4th of October 1957, the Soviet Union successfully launched history's first man-made satellite into space orbit around the Earth." and then, "the satellite, which the Russians have dubbed Sputnik is being hailed as a milestone in history"... strongly implying that it is a recent event.
Furthermore, after that there is a time and place setting subtitle superimposed over the footage that reads, "Coalwood, West Virginia October 5, 1957".

