Comic books in the United States in the format we know them today began with Action Comics #1 (1938), which introduced Superman and launched comics as a major industry - but Superman wasn't created out of whole cloth! Comic books started out in the 1930s as collections of comic strips from newspapers; some comic strips also ran in pulp magazines, and even before the advent of Superman there were characters with all the burgeoning hallmarks of superheroes in comic strips (The Phantom, Buck Rogers), and the pulps (The Spider, Olga Mesmer, Doc Savage). So it's important to remember that before superheroes were even in comic books, they were already beginning to be established in American culture.

However, superheroes were only one of the early genres of comic book. Like their direct predecessors the pulp magazines, comic books covered romance, westerns, crime, horror/weird terror, science fiction, sports, war, adult (the infamous 8-pagers or Tijuana bibles), etc. - and many of these other genres were incredibly popular and influential for decades.

The real rise of the superheroes came about with the advent of the Comics Code Authority in 1954 - earlier that year Dr. Fredric Wertham had published a book titled Seduction of the Innocent, which alleged that comic books contributed to juvenile delinquency - later research found that Wertham faked or misinterpreted much of his evidence - and in response most of the major comic publishers got together and instituted the CCA, which required members to abide by a Code - which essentially killed crime and horror comics, and drove Max Gaines and EC out of the comic business (he would go on to create Mad Magazine). The comic panic also spread internationally to connected markets, especially Canada (which, although it had generated its own local comics during WWII thanks to trade bans, was a major market for US comics) and Britain - the latter you can read about in A Haunt of Fears: the Strange History of the British Horror Comics Campaign, which is a very solid book.

The Code was such that it created a very limiting environment - one in which the rather hokey Silver Age superheroes were created and flourished, and which eventually gave way to more elaborate storylines and worldbuilding - Marvel Comics innovated the field in the 1961 when Stan Lee and Jack Kirby launched the Fantastic Four, and superheroes have benefited a great deal from being revisited and reinvented every generation - you can read about that in, among other places, Superhero Comics: the Illustrated History.

While superhero comics came to prominence in the late 1930s/early 1940s and continued to expand, other genres generally faded as demographics shifted - you could still find romance, sports, and western titles on the shelves in the 60s and 70s, but war comics largely fell off after the Korean War due to opposition with Vietnam (although surviving in such formats as DC's Sgt. Rock or Weird War). "New" genres also cropped up: sword & sorcery comics weren't exactly invented in the 1970s, but they didn't become a genre of their own until Marvel published Conan the Barbarian in 1970; talking animal comics began to take a more grown-up turn with the success of comics like Cerebus the Aardvark (1977) and Usagi Yojimbo (1984).

Horror comics were a hard sell with the CCA, and publishers like Warren got around them by publishing magazine-sized comics; in the 60s and 70s Baby Boomers that had grown up on pre-Code comics began to make their own "underground comix" - often featuring references to the old EC horror comics, as well as topical drug, political, and sex references; noticeably absent were superheroes, except for parody - you can read about that in A History of Underground Comics among other places - but, the underground comix scene gave birth to the independent or alternate comic scene of the 80s and 90s, where small-press publishers began producing their own comics in a range of genres - including superheroes.

The thing is that fans who had grown up reading those comics began entering the industry and writing and drawing their own storylines, or creating their own characters - and for many folks growing up, that involved superheroes - and superheroes were very marketable. Aside from just comic books, the characters and likenesses were licensed out for comic books, films, television shows, and an endless array of merchandise, which brought greater awareness and attention to superheroes - to the point that you could have television shows like The Greatest American Hero (1981).

Any farther along this line and I'm going to break the 20-year rule, but the gist is that the ground was laid for an audience to appreciate superhero comics before superheroes appeared in comics - through comic strips like The Phantom and pulp characters like Doc Savage - and benefitted from both marketability and a restriction in their competition which allowed them to flourish and crowd out many other genres. Generations of comic readers grew up to create their own comics and regenerate the field, to continue to draw in new interests - which isn't restricted to superheroes, but involves a lot of superheroes.