Maybe I played an FPS prior to this one, but the first one I remember was Halo:CE on Xbox. My stepdad bought an Xbox from his friend but it didn't come with any games (aside from Dead Or Alive Xtreme Beach Volleyball which was left in the disc tray and my parents never let me play lol). My mom took me to the store to pick out a game for it and there was a copy plastered in GOTY awards that was also sitting next to an Official Xbox Magazine issue that advertised a guide for CE on the cover. All that marketing made it seem like the best game ever so I went with that.
Took it home to play it and yea, fuck it really is one of the best games ever made! That moment you stepped out of the drop pod at the beginning of level 2 is still one of the craziest memories of my young life as a gamer. I remember just walking around and exploring that area over and over again. Trying to jump to the lower bridge (you can), staring at the waterfall for hours, trying to snipe the Banshees, choosing to run back and actually fight the patrol you're meant to avoid at the mission's start. I'd never played a game with a such a massive playspace before and the first person perspective just made me feel so small in comparison to it all.
I eventually got a lot of school friends into Halo since I was the only kid with an Xbox for a long while. Definitely blew a lot of our minds back in the day!