For a release date in 2019, if they want to age Indy realistically again - Crystal Skull aged him 19 years, since it had been 19 years since Last Crusade got released in 1989 - then this should be set in in 1968, 11 years since the events in 1957.
What was happening then? Vietnam spun out of control, the TET offensive surprising the US and it's allies. Would they tackle a quest there?