the ambiguous Clues to the Fictional Date
"United States Army" can mean AMY army of the several armies the United States had and has, such as the United States Volunteers in the Civil war. But it can also mean the regular army, the standing professional army, which is referred to as The United States Army. Thus a general in the United States Volunteers could have the initial USV after his title and a general in the regular army could have USA after his title to distinguish regular army generals from volunteer generals and distinguish both from militia generals.
O'Rourke was in the 69th New York Volunteers and also in whatever fictional regiment of regular army cavalry was in the movie. That leaves his statement that he was in the US Army for fifteen years ambiguous. He could have meant he was in the regular army for eleven years and in the volunteers for four years for a combined total of fifteen years and possibly served in a foreign army.
Or he could have meant that he served in the regular army, one possible definition of "the United States Army" for fifteen years, and in the volunteers for four years, making a total of nineteen years in US service, and was possibly in some foreign army earlier. Being old enough to have a son old enough to graduate from West Point (and thus usually twenty two) means that O'Rourke senior should have been an adult capable of being a soldier for some years longer than fifteen or nineteen years.
I'm not sure the creators of the film knew enough to appreciate the ambiguity of O'Rourke's statement.
If Fort Apache happens during the Civil War of 1861-1865 almost all of O'Rourke senior's regular army service would have been before the Civil war. If Fort Apache is set any time after 1876 all of O'Rourke senior's service in the regular army would be after the Civil War. If Fort Apache is set between 1865 and 1876 some of O'Rourke senior's service in the regular army would be before the Civil War and some of it would be after the Rebellion.
The break between the Collingwoods and the Thursdays could have happened in the Mexican war 1846-48 or in the Civil War 1861-65. 19 year old Philadelphia Thursday was already born when the break up happened but too young to remember Mrs. Collingwood. If the break between Collingwood and Thursday was fifteen to seventeen years before, the movie could be about 1861-1865 or 1876-1882.
The dress uniforms seen at dance indicates the movie is before new dress uniforms were adopted in 1873. The rifles used by the Apaches indicates the movie should be in the 1880s when many Apaches had repeating rifles.
The last year when the hostile leaders Cochise, Geronimo, Satanta, and Alchesay were all alive, free, and hostile to the United States was in 1869. In that year the White Mountain Apaches made peace and Alchesay went on to be sergeant of Indian Scouts and earn the Medal of Honor. Thus some may suppose that the film opens on Washington's Birthday in 1869 and the battle is a few months later.
I trust this shows that we don't know when when Fort Apache fictionally happens.