I guess the ones I didn't hunt for were the quickest since you don't get a lot of encounters when casually playing through the games, especially if you use repels.
Random:
My first shiny was a random Audino that I found while grinding my team for the next Gym on my first Black 2 playthrough, I was in the grass for maybe 20 minutes just encountering Audinos since they give a lot of EXP and the shiny just showed up. But that was around the middle of the game so if we are going by the earliest I ever found one in the casual playthrough then I have 3 that come to mind: a random shiny Wurmple before even the first Badge in Alpha Sapphire, a random shiny Pikipek in Sun on the first island right after I got the Tauros Ride and a few years ago I was also (un)lucky enough to see an uncatchable shiny Weedle in the Old Man's catching tutorial of FireRed.
Hunted:
My fastest shiny hunts were usually with different shiny hunting methods. I got a shiny Flabebe from the 3rd Egg with the MM and I also found a shiny Dusclops in Friend Safari in like two encounters and I wasn't even trying to shiny hunt, I just wanted to see all 3 possible Pokemon in my new Ghost Safari. I also got Luvdisc, Horsea and Magikarp with Chain Fishing Method in under 25 FEs.
The fastest full ~1/8k odds shiny that I actually hunted for was a shiny Growlithe in White 2 and I got it in under an hour and maybe around 600 REs.