Something I've occasionally done is get players talking before everyone even knows what the game and setting is. Like, when we know a campaign is winding down, we have a point where we all talk over what we're going to play next. As we settle on a game, people talk about who the PCs will be as a group, and who their PC might be. I've seen a similar pattern when doing Powered-by-the-Apocalypse games, like Monster of the Week. There are a set of playbooks/classes, but at the start, we don't know if we're playing in 1950s Mexico or near-future Japan. During the session, the players and GM come up with a specific setting as a group, then work out what their PC is like.

I was introduced to D&D in 1975 when I was in preschool, because the older brother of my best friend played it. My best friend and I then called our make-believe games "playing D&D". A few years later I got my own Basic Set and learned the rules for real. I've played over a hundred games since then -- ranging from tactical games to Nordic larp. The single game that I've gone back to the most is Call of Cthulhu, but I've done a lot of many others - HERO, GURPS, RuneQuest, D&D, Amber Diceless, FATE. My current go-to is Savage Worlds, but I also just tried Lancer. The Bartle Test doesn't really work for me, since I tend to do very different things from one game to another.