I started around possibly 2000/2001 when a much older nephew started up his Nintendo 64 and played Mario Kart 64. Around this time as well at another family member's house, I played Super Mario 64 and I was blown away at how life-like the games was for the time.
I would not own my own game console until 2007 when my dad's coworker gifted me a Nintendo GameCube...
2006-2007 when I was like 7. I had wanted to play Pokemon games for the longest time, but I never got a Gameboy and instead started with a DS and Diamond.