id and/or Bethesda have never explicitly stated when it is set. The original id games are in the same universe though - it's been confirmed that B.J. Blaskowicz from Wolfenstein 3D is Commander Keen's grandfather, and Commander Keen is either Doomguy's father or grandfather (i'll go with father, as that's the more common conclusion).

Since Wolfenstein 3D is set around the mid 1940s, B.J's son/Billy's (Commander Keen's) father was probably born around that time, maybe from around 1942-1962, due to the fact that the original Commander Keen is set in 1990, and 20-40 is a pretty common age to have a child at during the time, Billy Blaze being 8 (born 1981-1982) in the game.

We can assume that Billy had a child from around 25-40 due to that being a more common age to have children at during the time he grew up.

This would have Doomguy born from around 2007-2022, and Doomguy is estimated to be around 20-30 in Doom 1, so my estimate is that the game is set from around 2027-2052 - which doesn't really narrow it down, lol. But anyway next year we could be approaching Doom guys be careful and see if you can get your hands on a BFG