Depends where, here in Europe (my bias is centered around France and other Francophone countries, AFAIK Italy has had a similar early exposure), we started having japanese anime broadcasted on major television channels as early as 1978.
Things like Goldorak (UFO Robot Grendizer), Albator (Space Pirate Captain Harlock), Dragon Ball, Knights of the Zodiac (Saint Seya), Sailor Moon, along with many many children's shows, including numerous adaptations of Western Litterature classics, or various Euro-Japanese collaborations made up a sizeable chunk if not the majority of broadcasted animation at a time, chiefly on kids time slots and/or part of kids shows.
Anyone who grew up in the 80s and 90s received a substantial dose of all of that as they grew up, but by the late 90s it more or less stopped as far as major channels and kids slots were concerned, with the notable exception of Pokemon. Classics would see reruns, and we had the likes of Gundam Wing, Evangelion, Cowboy Bebop and Visions of Escaflowne, but those were first broadcasted in late afternoon slots (typically on the free slot of a major paid channel, before seeing reruns on cable).
In the 90s manga publication had started, with both major and niche editors gobbling up the catalogue of classics and quickly venturing into novelties, and choice and popularity exploded in the 2000's.