Shooting has been with the US Olympic Team since the first Modern Olympics. Back in the 80s, I remember seeing a cheesy mini-series about the Greece Olympiad of 1896 and I was surprised to learn about the American Shooting team, Like many others, I barely knew that there was shooting in the Olympics except Biathlon in the Winter version.
John and Sumner Paine were brothers who participated in the first Modern Olympiad in Athens, 1896. Both came home with gold medals and Sumner won a silver medal losing to his brother.

Same as the rest of the US Team, they were not very clear what the rules were and according to Olympic.org:

Uncertain about the weapons or the number of rounds required in Athens, the Paines packed an entire arsenal: two Colt army revolvers, two Smith & Wesson Russian model revolvers, a Stevens .22 calibre pistol, a Wurfflein, two pocket weapons, and 3,500 rounds of ammunition!

Their first event was the 25 meter Military Pistol which John won Gold and Sumner won Silver and they literally trounced the competition. The next day, only Sumner competed in the 30 meter Free Pistol because they felt another double win would have been a slight to the rest of the competitors.

So, even if the “Betters” shun our Olympic shooters from the mayor TV coverage, feel proud that our Olympic roots run as deep as many of the classic Olympic sports and certainly much deeper than many of the stuff they have been shoving lately like golf. I expect synchronized basket weaving any day now.

PS: A quick note. Although now classified as Gold or Silver, the first Modern Olympics issued a Silver medal and a branch of olive to the winner and a copper medal to second place. The gold-silver-bronze medal system did not happen till the St. Louis Olympics of 1904.