When Does the Stage Musical "Back to the Future: The Musical" (2020) Take Place?
"Back to the Future: The Musical" is a comedy science fiction stage musical written by Bob Gale with Glen Ballard and Alan Silvestri [adapting "Back to the Future" (1985) by Bob Gale with Robert Zemeckis] and first performed March 11th, 2020.
It takes place in the years:
We know this because Doc Emmett Brown's time machine's source year and destination year are stated several times.
Then, at the beginning of act 2, Doc Brown says, "October 26th, 1985 AD", when referring to the time Marty left from at the start of the story.
1985 AD/1955 AD
We know this because Doc Emmett Brown's time machine's source year and destination year are stated several times.
Partway through act 1, just before the first instance of time travel in the show, Doc Brown speaks "November 5th, 1955 AD" into the voice activated car time machine. Then, once there, as Marty McFly walks into Hill Valley, the inhabitants of the town sing the sixth song, "Cake", which includes the lyric "1955 has been a banner year!"
Then, at the beginning of act 2, Doc Brown says, "October 26th, 1985 AD", when referring to the time Marty left from at the start of the story.
There was a Broadway revival in 2023. 
