I'm assuming pellet guns don't count - or we'd all have the same story.
My first bird with a firearm (this is going to be embarrassing) was a Spruce Grouse with a .300 Weatherby Magnum. I know....WHAT???
Well, I was moose hunting. 16 years old, first real hunt, hunting with a gun I borrowed from my Uncle's friend (twice removed). Here I was, marching around in the bush north of Grande Cache, not seeing much of anything (except grouse). One afternoon it occurred to me that I hadn't so much as fired the rifle, yet. What if I saw a moose? I wouldn't even know if the scope is sighted in!
While I was contemplating this conundrum, I chanced upon a spruce grouse that hoped I hadn't noticed it. As it stood frozen in the middle of the path, I put the grouse's head right in the cross hairs and pulled the trigger. I knew nothing of stance, mount or recoil, so I was taken completely by surprise as the Weatherby erupted in my hands. I confess, it knocked me off my feet.
All I ever found of that grouse was one leg and lots of feathers.
My first bird taken with a gun was a Blue-winged Teal with a Cooey 16 gauge single shot.