Why do you prefer '62?
My preference personally would be anywhere from 1959-1961...I cut it off at '61 because '62 is the year of the Cuban Missile Crisis; In America, at least, this is culturally one of the first defining events of the '60s. Pop culture didn't really change much roughly between '57 and '63, which is why 1960-1963 is sort of a forgotten time; It was basically a continuation of the '50s. I mean, I am open to anything up to 1965...But I'd prefer no later than 1961.
I have to admit, it will feel weird seeing, say "Egypt, 1961" at the start of the next movie. I have always wanted to see Indy in the early '60s, but I will admit it will feel different. The '50s are an easier sell because they're a less modern period, a more pulpy time (it being the era when quite a few of the films which inspired Indy came out). The '60s start to take us into modern history...Anything in and after 1965 is to me modern history.