It could've been three different games, and I'm not sure which to call the first.
Super Smash Bros., I think, at a random party? I was six years old or so and I just mashed random buttons, and got angry when I lost (almost always).
Or Pokémon Gold, which my sister and her friend would play and I'd watch. But I never played so maybe that doesn't count.
The first Nintendo game I played was prooobably Pokémon Sapphire. I can't remember that clearly, though.