Anime became more mainstream in the U.S. long before Toonami.
Space Battleship Yamato/Starblazers started the first real penetration of Anime into U.S. culture (there was Anime in the 1960s too with
Speed Racer/Mach GO GO,
Tetsujin 28/Gigantor and
Kimba The White Lion but it wasn't really recognized as such at the time by many in the U.S. audience) in 1978 and
SDF Macross/Robotech and
Captain Harlock and the Queen of 1000 Years continued the trend in 1984 - and the film
AKIRA made a splash and raised awareness in 1988 followed by
Sailor Moon and
Pokemon in the early 1990ies.