There has been selective service registration since we went to the all volunteer military in the early 70’s.
Wrong!
I turned 18 in 1977, and there was no selective service registration requirement at the time.
I believe the registration requirement went into effect in 1978, because (as I recall) I just missed having to register by a few months.
I know it was definitly required for people that turned 18 in 1979, as I know at least one person that did have to register in 1979.