I know that they would have to rewrite history but that has not stopped them before, I just think it should be mentioned that one of the biggest find in the history of archeology was The Dead Sea scrolls and they were found in 1947 and that fits nicely in Indy's time line.
Add some Nazi or Communist villains, some secret magical powers, some traps, and a plot reason why Indy needs to find them but doesn't take credit in the end and you have got yourself a movie.