From 1964, with the Beatles and the Beach Boys, through about 1967, with Spanky and Our Gang and the Strawberry Alarm Clock.
Then, the nasties started to show up, feasting on all the idealism and naiveté. Sirhan Sirhan, James Earl Ray, Charles Manson, the Zodiac Killer, the Black Panther Party, the Weather Underground... the whole beautiful thing turned into a hateful disaster.
But for a few years...
I guess it was the period of recovery after JFK got shot. Kind of an Indian Summer of our culture.