It's hard to point at one game, because I had peripheral and momentary experiences with many before I sat down one-on-one with enough capability of playing a game with little help. I was born in the early 90's. I liked the characters of Mario and Sonic from the cartoon adaptions and merchandise from that era, before even getting my hands on the games. My parents would walk me through arcades. My first cemented memory of being around a console was watching my god brother play Sega Genesis. He played a lot of fighters with the family that were his age (tweens/early teens). I was shown Sonic upon request. I didn't do much more than observe, but I was mesmerized.
My god brother's parents gave me his NES when I was about 4 with dozens of classic games (his parents didn't want him hoarding a collection of old hardware and software, and my parents would have the same feeling with my games until I was mostly paying for my own entertainment). I was given almost all the iconic first party stuff and lots of good third party titles. I popped in a Super Mario Bros game first, iirc. Even though the SNES/Genesis/Gameboy were the hardware of the time, I so appreciate my introduction to Nintendo now.