Close. It was invented in 1960, prior to the hippie movement and referring to their predecessors, the beatniks of the 1950s.

I wasn't alive so I'm just going off casual web searches, but most people seem to credit this 1969 book: https://en.wikipedia.org/wiki/The_Making_of_a_Counter_Cultur.... It was not the literal first usage, but the word was definitely not widely known before the 60s: https://books.google.com/ngrams/graph?content=counterculture.... But I said literally and it wasn't literally true, so my bad.

I'm guessing beatniks in the 50s myself.