Pulling from Wikipedia, since I'm too lazy to dig up all of the primary sources:
The origin of HIV is not much of a mystery. Based on the genetic dispersion of HIV strains, the virus entered the human population somewhere in West-Central Africa between 1885 and 1925, from an infected chimpanzee (most likely from a bushmeat hunter bitten or wounded by the animal).
Therefore, the disease being present at some level throughout the 20th century is inevitable. The extent of the epidemic can be changed considerably. OTL it was dispersed well beyond sub-Saharan Africa by the late 1950's (based on forensics of cases that weren't diagnosed at the time); with the first cases arriving in the USA via Hiati in the 1960's.
Back to the OP question:
HIV is also transmitted by infected blood transfusions (happened until the late 1980s, OTL) and dirty needles. To blame the Sexual Revolution, you'd have to convincing demonstrate that it corresponded to an increase in risky sexual practices (rather than, say, just recognition of them); and show that many more of the first cases were transmitted by sex rather than by drug needles. Blood transfusions aren't significant until there are a large number of cases, by which point the epidemic has already happened, so it doesn't change the number of cases by more than a factor of a few.