The main story of Indiana Jones and the Dial of Destiny is set in 1969.
The film begins with a 1944 sequence involving Indiana Jones and Basil Shaw during the final years of World War II. It then jumps forward to 1969, when an older Indiana is preparing to retire from teaching in New York. The story connects his personal life to the Apollo 11 era, including the public excitement surrounding the Moon landing.
The 1969 setting places the adventure at the end of the 1960s and gives the film a different historical atmosphere from the earlier entries. Instead of the prewar and early postwar environments of several previous adventures, the plot uses the space race, changing universities, and the aftermath of World War II as major context.
1944 is therefore an important year in the film, but it belongs to the opening flashback. The principal adventure takes place in 1969.