This one depends a lot on how you define fanfic.

If you're going by "transformative work in conversation with other transformative works based on a shared canon," it was probably some fairy-tale or bible-story picture book from before I can remember. (Honorable mention to Monsterpiece Theater which probably shaped more than I will ever realize I ever learned about storytelling, but it's theater not text, so it doesn't count.)

The first things in the sense of "derivative work of a specific copyrighted canon" that I interacted with in what I now recognize was a fairly fannish way were Heidi's Children and Heidi Grows Up, by Charles Tritten, which were continuations sort-of-with-permission after the author's death. In particular they taught me that just because one particular author thinks something is canon it doesn't mean it actually is. :P It also taught me that it's 100% legit to respond to a book you like by writing your own sequel, so from somewhere around that time there are scribbled bits and pieces of the continuing story of Queen Amethyst and King Peregrine of Ambergeldar.

By later elementary school, I'd decided I wanted to be A Writer, and was subsequently exposed to enough "how to write" advice to make me self-conscious about originality (and self-inserts. and femininity), but shortly thereafter I fell into Star Trek and Star Wars and was reading all the published tie-ins I could get my hands on, so that didn't last long. (I learned about 'slash' from authorized published Star Trek fandom books. And Kirk/Spock from the movie novelization...) Some of the authorized anthologies were culled from zine fic and had all the requirements for fanfic (written by fan authors for fan authors, full of fandom tropes, etc) except that they were (sometimes retroactively) approved by TPTB and published. Most notably for Star Trek: the New Voyages anthologies, and I swear there was at least one Star Wars anthology in the 1990s that included fan content, because I don't think I could have possibly have imagined that incredibly trippy Corellian pastiche of Der Erlkonig, but nobody else seems to remember it? The main thing I remember about these is that the fan-written works, while often not as polished, always felt way more intense than other books, and at age twelve or thirteen I didn't know how I felt about that.

Anyway, it was also around this time that I read my copy of Heinlein's "The Number of the Beast" until it literally fell apart, because crossovers + queer poly. I have weaknesses, okay. (And after that, any pro sf author talking crap about fanfic was going to get hit over the head with said falling-apart book until they stopped.) (I don't care what your objection to fanfic is, Heinlein did it in that book) (including exposing children to it at a probably too-young age...) (It's okay, it was a pretty soft book by that point.)

My time in anime fandom was actually fairly fanfic-free, but shortly thereafter I got into webcomics fandom, which at the time was a place where the lines between fan creators and canon creators were very blurry, because pretty much anyone could attempt to create a webcomic (and did), and the fandom activity all took place on official forums that were modded by the canon creators, and it was all very slipstream. I'm sure I read some webcomic fanfic on the Keenspot forums, but if I did, I cannot tell you anything about it, except that it was almost certainly more heavily influenced by anime fandom than Western media fandom. (I also had my only experience with forum-based roleplay there.)

At the time, most webcomics had a sort of proto-blog where the comic creator would post life updates and behind-the-scenes stuff about the comic, and at some point, some webcomic I was reading (Queen of Wands, maybe? That sounds right but it probably isn't) posted their Favorite Fanfic, and it was for a book I'd just read and desperately needed more of, and that is what I usually consider officially My First Fanfic.

It was And When He Falls, by torch, Aziraphale/Crowley. I have just re-read it and it is still good; a better First Fanfic I could not have possibly found! (It must have been pretty new at the time, too.)

I didn't go on from there and read more in media fandom stuff. Not sure why, except that torch didn't have anything else for fandoms I knew, and I was spending pretty much all the internet time I could get keeping up with about 75 webcomics on dial-up.

So I didn't really fall headfirst into being a fanfic fan until several years later, when I was at college, and a bunch of us were going to see the new Harry Potter movie, but I hadn't brought my copies of the books to college with me, so I couldn't re-read them in preparation for the movie, but I certainly wasn't going to go to the movie without reinforcing the buttresses of book canon in my mind, so I decided to read some fanfic instead.

I ended up on this archive that I can't for the life of me remember the name of. It had a name based on a place in canon, like a lot of them did at the time, but it wasn't any of the ones on the fanlore list of Harry Potter archives. It was specifically aimed at adults, but more 'adult themes' than 'NC-17' and I don't think it was the Restricted Section - RS.org would have been very very new at the time, and I don't think this was, and I didn't have to register an account to read, and also I'm pretty sure RS was an efiction archive, whereas this one gave off the distinct vibe of everything being hand-coded (and possibly of being invite-only.) It only had a few dozen stories on it, by a dozen or so authors, nearly all of them novel-length, but darned if I can remember any of the specific stories; I think a lot of them were crossposted other places too. Multiple pairings and eras, including slash and het and even gen iirc (Is this ringing a bell for anyone else? No?) (ETA: Hah, never mind, it was Diagon Alley, it was on the list after all, I just skimmed it over because the name seemed *too* canon to be the right one. But it was that.) (ETA2: Fuck me, the Draco Trilogy is still readable in its wayback link from fanlore. *eyes first ever archive* *eyes giant to-do list*)

Anyway, I burned through that archive in about a weekend, and after that it was all fanfic, all the time, forever.