I "technically" discovered anime via toonami is a kid around 1997 (at age 7). Although I didn't have any knowledge about the term "anime" nether do I know what it is. I just thought of it as a regular cartoon action show. It wasn't until late 2004 (7 years later) as a freshman in highschool (9th grade/14 years old) when a friend of my brother's introduced us to drawing anime (and eventually anime/japanese music in 2005 by letting us borrowing some of his burned CDs. We would then use his CD's and save the songs into our Xbox lol). We eventually watched anime via Adult Swim as well. A few more years passed by (hello 2007 and 2008) and we were introduced by one of my father's old college friend who happens to have a son who loves anime as well. He introduced us to LimeWire (which, as you know today, does not exist anymore), ecchi anime (Tenjou Tenge and Jubei Chan), and more anime music. That's how I (and my brother, RIP) discovered anime.
Fun Fact
Discovering anime has actually lead us into Dance Dance Revolution (DDR) in late 2005 (which has a lot of Japanese music) and we loved it. A year later (in 2006) when we finally have high-speed Internet for the first time, we took advantage of the Internet mainly watching YouTube videos of anime (including some AMV), mainstream music, and DDR gameplay (some of those videos were actually Stepmania and ITG, but we didn't know at the time). Eventually, we were lead to a video of a Stepmania player named Arch0wl playing quasar in 1.5x speed receiving all perfects resulting in an AAA rank. At the end of that video, displays a website called Arch0wl.com. We didn't check the website at first, but my brother (RIP) eventually did when he was sick and was absent from school (and I would assume that he watched that video again and checked out that link which leads us to, you guessed it, Flash Flash Revolution (FFR) in late 2006). He ended up trying the game out and eventually introduced the game to me and I ended up loving the game. This eventually lead us to Stepmania a month or so later in 2006 which contained more music -> then to more anime and anime/japanese music -> and from there, everything just branches out from 2007 to 2011 such as touhou, eroge (didn't know it called a visual novel/eroge at the time. I only thought of it as a game lol), Japanese game shows, anime streaming and anime (English dub only) downloading websites, and so on and so forth. I did discovered osu! around 2010, but the game didn't interest me at first sight, so I didn't even bother with the game and skipped it (only to end up playing it a year later (Hello 2011) and ended up loving it to death lol) -> more touhou in early to mid 2011-> eventually giving osu! a try in September 2011 (a month after my brother started) in a new laptop (since multi-accounting was forbidden and we were smart enough to not play at the same computer lol). The first thing I discovered in osu! was nightcore music, much more eroge OP music/video, much more anime/japanese/touhou music and their respective videos, much more anime, etc. Over the years of playing osu!, I ended up becoming a weeaboo hahaha (what has osu! done to me XD). Anyways, I will end from here, thanks for your time.