I believe so, if not my father still does; he can't remember which was the first I ever shot, and I certainly don't as I was about 5 at the time and had shot several firearms by the time I was 6. However among the first few guns I ever fired were a Ruger MarkII(the first gun my father ever purchased himself when he was 18 in the sixties), a Colt Gold Cup .45ACP 1911 (present from my mother to my father when he graduated from law school), a S&W 9mm semi (my father used as a reserve police officer in MA), and/or a Ruger 9mm/.357mag convertible revolver. My father still has the Gold Cup, the S&W 9mm, and the Ruger revolver, he gave me the Mark II a couple years ago. So basically yes I have or my father has the first gun I ever fired; hopefully I or my siblings future children will fire the same guns at a young age; although now the family collection has grown they may end up firing others first. As a matter of fact my father is building a custom 9mm 1911 for my sister right now, I wish her fiance was more into guns, but at least he isn't an anti and enjoys shooting now and then; so their kids won't miss out on the training; guns for christmas or other holidays and overall enjoyment of being shooters. I plan on doing my uncle job there.
I unfortunately don't have the first firearm I ever owned - at least in working condition, when I was about 6 I was given a .22lr single shot rifle under the Christmas Tree. That rifle more or less began to fall apart several years ago and has now been replaced with a duplicate in working order, the original much to my chagrin is no longer in a very useable state.