The anniversary is indeed for the Super Mario series instead of the character, but anyway, congrats.
And I really don't remember that. All I know is when I started gaming, we didn't have Nintendo's ourselves. I had my mom's Odyssey2 and my aunt had the NES and SNES. I didn't get my own Nintendo system until I got the GameBoy likely in late 1995. I can be pretty sure about that because I got it (a classic, transparent model) as a gift from my would-be stepdad when he first started seeing my mother and I already had it and a couple games on a holiday the following year.
I'm not sure about the timing, but I think the SNES was already out at the time I started gaming, it was probably around 1993 at the age of 5, but it could be even sooner. I just don't know. Still, Duck Hunt on NES, or a certain shooter game on Odyssey2, is likely my very first game, I doubt she would have let me and my cousins play on her fancy SNES until some years later. I do remember having a big interest in A Link to the Past as a small kid though and always wanted to watch her play it. I likely also watched her play Super Mario World, but I never really got into that one.
Anyway, if Duck Hunt is my first game, then it stands to reason Super Mario Bros. was my first Mario game, because it was on the same cart. I'm not sure though, and my first real memory of playing Mario is playing Super Mario Bros. 3, on the same NES, but I'm not sure about the timing. I liked it, but didn't really think much of it until the GameBoy Advance port a decade later, when I started to see the game for the masterpiece it was.
On the old GameBoy I got Super Mario Land with it, and I definitely remember playing that a lot, but it was probably after I had played the NES Marios. I remember being pretty bad at it, and I never beat it, but I liked it's locales a lot, especially the Egyptian style pyramid levels. It's funny though, it seems like SMB and SMB 3 at the time didn't resonate much with me, though the latter still moreso than the first, seeing as I have only such a vague memory of playing them, while I can easily remember tons and tons of playing Duck Hunt and the black-box Soccer on NES or SML on GameBoy instead.
With Yoshi's Island though, shortly before the release of the N64, my fondness of Mario was finally and definitively realized. The game was immediately one of my all-time favorites and probably even my all-time favorite game, period, for a short period of time. Then, it even went past that brilliance with the seemingly perfect Mario 64, which made me revisit older Mario games, and made me get spin-offs like Mario Kart. After Mario Kart 64 I even went back to the SNES to play the first Mario Kart. After that I just got every Mario platformer and every Mario Kart that would get released and a host of other spin-offs. It took some years, but finally, halway through the '90s, Mario, and thus Nintendo, was there to stay.
Here's to another great 30 years of games!