I think the first games I played extensively probably has to be Need for Speed Rivals, Hawken, and Rayman Legends
One of the first games I played on my own console at least probably has to be Rayman Legends on the Xbox Original (Not to be confused with the Xbox 360 which means one, or the Xbox One which is yet again means one, or the Xbox X series which could also mean one.) *sorry I really don't like Xbox* I used to play that game so much though, at least I did till the disk-tray stopped opening, haha.
I also strongly remember playing the crap out of Need for Speed Rivals when the Play Station 4 first released in 2014. That has to probably be the first racing game I ever played other than 4x4 Evo on the Xbox Original. I remember always raging because my brother played the game as well and was always better than me just because of him being older and playing racing games for more than double my lifetime.
I also remember in 2013-ish when I was probably around 6 or 7 years old I would sneak out of my room into my parents closet and steal the Verizon WiFi router (Which was very shitty and way overpriced) and I'd go sneak into the kitchen and boot up Hawken on the kitchen PC at 9 or so PM (I know such a rebel) and I'd play that for probably at most an hour before I'd get caught by my dad and get forced to go back to sleep, Those were good times I had little to no responsibilities, now I'm 16 work 2 jobs, go to school, and manage a 9 acre property.