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boxingcardmanThere is no answer, really, until you define "pack". As has already been noted, the first baseball cards inserted with product were in the 1880s.
My first pack was 1970 Topps. I think I got one or two packs that summer. In 1971 I really took off. Other big years were 1975 (my parents bought me two boxes as a birthday present) and 1977, where I'd buy a pack as often as possible at the candy store near my school. From 1977-1978 I didn't buy packs at all because my uncle did legal work for Topps and sent me a huge box of their products including a couple of vending boxes every summer. In 1979-80 I bought lots of packs. I fished a lot for error cards in the 1981 offerings and more or less stopped buying modern after that.