https://docs.google.com/document/d/1I_5GfGqfidbrfhpwzMvsccjDxjCd39M6nERp99wVEBQ/preview

"History of Trap Shooting Organizations" (mostly - I tried to confirm the dates he listed from the Sporting Life Archives) by Ed Muderlak

The first "International Clay Pigeon Tournament" (or inanimate target tournament) was run by Geo. Ligowsky's and J. E. Blume's National Shooting Association in Chicago in 1884; the second International Tournament was in New Orleans in 1885. Ligowsky tried to sell stock in his association, but was unsuccessful. Ligowsky's NSA was formed to promote his clay targets.

C. W. Dimick of United States Cartridge Co. and other manufacturers' reps (including Winchester and UMC) founded the American Shooting Association Feb. 11 1889, and Ligowsky's group gave way to the power. S.A. “Tuck” Tucker, Parker's sales agent and Capt. A. W. duBray (then a sergeant in the U. S. army) were consulting board members of the newly formed ASA, and “Tuck” wrote the handicap rules. (Dimick was President and L.C. Smith was a Director.)
Live birds were still the popular targets with slight but growing interest in clays.

The ASA dissolved in 1892 and, in turn, the Interstate Manufacturers and Dealers Assn., “Interstate Assn.” took over organized trap shooting. The Interstate Association’s purpose was “for the encouragement of trap shooting, in giving tournaments to foster a sport that is deservedly popular to bring together experts, semi-experts and novices, to safeguard the interests of both, and to show how a large trap-shooting event should be run.” It quickly organized the first Grand American Handicap at Live Birds, under Revised Hurlingham rules, for spring 1893. Twenty-one shooters paid $25 to compete. In 1894, first place was awarded $500 and guns were limited to 12 gauge and 8 pounds. The last GAH at Live Birds was in 1902 at Kansas City with about 450 contestants.

The short lived American Trap Shooters League was organized in 1895.
http://library.la84.org/SportsLibrary/SportingLife/1895/VOL_25_NO_03/SL2503014.pdf

In 1919 the Interstate Assn. board met in New York, and reorganized as the American Trapshooting Assn. In 1923, it became the Amateur Trapshooting Association, “The ATA."