There's two "times" critical to accuracy. Both are typically measured in thousandths of a second. This thread's about the most common one, how long it takes from when the sear releases the firing pin (or hammer) and when the firing pin strikes the primer.
The other one's "barrel time." How long it takes from the firing pin impacting the primer to when the bullet exits the barrel. For a given centerfire cartridge and load, the longer the barrel the longer the barrel time. It's typically between 2 and 3 milliseconds. .22 rimfire ammo's longer; they shoot slower.
An interesting thing was done some years ago for high end match rifles made in Germany. Anschutz (well known in international rimfire competition) had developed the fastest trigger-firing pin system on earth; a bit over 1 millisecond lock time. But their 26 inch barrels had a long barrel time. It was hard for the kids on Olympic teams to shoot goood scores from standing. They had to hold still seemingly forever after the sear released. So Anschutz shortened the barrels to about 19 inches which greatly reduced barrel time. A tube was added to extend the front sight back to the original sight radius.
Now the Anschutz barrels are back to 26 inches. I've no idea why. Maybe it's an accuracy issue.
US Navy Distinguished Marksman Badge 153
Former US Navy & Palma Rifle Team Member
NRA High Power Master & Long Range High Master
NRA Smallbore Prone Master