While I watched
Pokémon and
Yu-Gi-Oh! on TV as a kid, I think the first anime I watched while
knowing it was anime, was probably
Naruto on Jetix and it just kinda went from there - with Propeller TV having their Anime Network block and Rapture TV showing
Fullmetal Alchemist helping me diversify my palette, before the Anime Central channel came along and I fully embraced my weebdom on their forums - and then learned more from the web.
These days, with broadcast television being less important and social media being more-so, I imagine that someone is more likely to be exposed through seeing screencaps, gifs or...urgh, memes, posted on Facebook/Twitter by people they follow, then investigating once something grabs their interest. Due to increased presence at events like Comic Cons, I'd say that anime has almost become a third pillar of typical nerd culture too, hence why larger geek-sites like IGN have increased their coverage of late.
I think a considerable obstacle, is the fantastic (and unfortunately, true) observation
@Rui made about the way anime fans are perceived in the mainstream. While the whole "anime is just porn!" sentiment was in decline compared to a few years ago, I've seen a resurgence due to the supposed rise of the alt-right, with more "progressively-minded" people using "anime avatar!" as an instant put-down, for example. On that note, I believe Jerome has a very valid point about the number of otaku-orientated titles being produced, with the mainstream successes (
Attack On Titan,
Yuri!!! On Ice) being too few and far between. The recent theatrical pushes of more artistic films like
Your Name,
A Silent Voice and
In This Corner of the World and the critical acclaim the acquire (Mark Kermode loved
Your Name), will help raise awareness and hopefully lead to growth of the industry.
Rui's observation about advertising is also spot-on, although rather than the blame being in Crunchyroll's corner, I'd turn my attention more to the big players - Netflix, Amazon and Universal. All three have huge social media presences with a diverse range of followers, but when have you ever seen even a tweet about
Aijin,
Kabaneri or
Seraph? It could be that they don't consider any possible return as worth the money, especially when they could allocate resources to
Marvel's Iron Fist or
The Grand Tour for example, but with the exception of Universal, their messaging is terrible
even to us, so how are the non-converted expected to find shows buried in categories they may not normally look at?