Has there been any confirmation as to the approximate year this show is supposed to take place? I just finished the first season. At first, I was thinking that it was set in the 1960's, but the further I got, the more confused I was about the time setting.

In Chapter 7, Amy mentions contacting her husband and mentions email as one of the options since David warned that calls would be monitored by Division 3. While the first email message was sent in the early 70's, it wasn't really available to the general public, which Amy and her husband are likely part of, until the early 1990's. Even though this series is not connected directly to the movies, the X-Men movie universe seems to be more technologically advanced than the real world, so the general availability of email might not mean anything.

They mention that Oliver has been stuck in the astral plane for 21 years, but asked David if the free love movement of the 1960's is still a thing. That would place "present day" in the show at least in the 1980's if Oliver had actually been stuck for that long.

In Chapter 8, David tells the team, "War is over if you want it." That phrase was used in an anti-war marketing campaign by John Lennon and Yoko Ono starting in 1969, and spread further with Lennon's song "Happy Xmas (War Is Over)" in 1971. If that quote was supposed to be a topical pop culture reference, that would set the show in the early 1970's.