No paper trail needed. We have two samples from infected people, one from 1959 and the other from 1960. The '59 virus is a Family I virus (think first generation), while the '60 case is a Family II virus. Knowing that the rates of genetic drift for a virus like HIV is fairly constant, and that it would take a certain amount of time for the Family II virus to take on its distinctive characteristics, we can logically determine that the Family I virus entered the human population about the turn of the century. I know this may all seem a little esoteric for those of you not in the science trade, but this is how modern virology is done. Not that it will convince the tin foil hat crowd.
HIV's not-so-ancient history