The time and place
The protagonists travel from the lonely site of the Gila Valley Massacre to the nearby town of Silver City (possibly Silver City, New mexico Coordinates: 32°46′41″N 108°16′27″W) to Tucson, Arizona (Coordinates: 32°13′18″N 110°55′35″W) which should be no more than 20 or 30 miles from Gila Valley to Sierra Blanca in West Texas (Coordinates: 31°10′55″N 105°20′27″W).
That is a journey of several hundred miles. It is 404 miles via I-10 east from Tucson to Sierra Blanca. You will note that the distance between Silver City, if the real one in New Mexico, and Tucson, Arizona, is a lot farther than a stage could travel in a day - 202 miles via I-10.
Sergeant George Lake was a veteran of the Civil War, and Barton MacLane (b. 1902) turned 54 in 1956, so Backlash should happen in or before 1901.
Jim Slater was a Rebel in the Civil War of 1861-65, and portrayed by Richard Widmark (b. 1914) who turned 42 1956, in the year that Backlash was released. Thus Backlash should probably happen in or before 1889.
Major Carson was probably a former Rebel major in the Civil War. Since Roy Roberts turned 50 in 1956, and Rebel majors were usually at least 30 years old, Backlash should happen in or before 1885.
Karyl Orton was married before the Civil War ended in 1865. Her husband did not return to her after the war, and was one of the men killed in the Gila Valley Massacre. Since Donna Reed turned 35 in 1956, and a bride would usually be at least 15, Backlash should happen in or before 1885.
Colonel Welnick probably had a high rank during the Civil War. Since he was portrayed by John Maxwell (b. 1918) who turned 38 in 1956, he was a very young colonel if he was the same age as his actor. The sooner Backlash happens after the Civil War the more plausible that would be. General Ranald S. Mackenzie, born in 1840, was probably the youngest Colonel in the US army and turned 38 in 1878, so Backlash should happen in or before 1879.
So the Civil War ended in 1865, the Gila Valley Massacre happened in 1865 or later, and Backlash happened an unknown period of time after the Gila Valley Massacre, in or before 1885, and maybe in or before 1879.
Sergeant Lake expected that hundreds of hostile Apache warriors could be at the trading post the next morning. Most of the Apache groups in Arizona were hostile all during the 1860s. In 1871-72 peace envoys Vincent Colyer and General Howard made peace treaties and all the Apaches except for the Tontos made peace - the Tontos were defeated by General Crook in 1872-73.
Thousands of Apaches remained at peace ever since. From 1873 to 1876 there were several outbreaks of hostile Apaches, so at any one time the total number of hostile Apache Warriors might have been somewhere between 0 and 200. So Backlash should be before 1886, and probably before 1873 - if it happened in the real west instead of the reel west.
Sierra Blanca is a small town without a railroad. But Sierra Blanca was founded in 1881 when two railroads met there, and so never existed without a railroad. So Backlash could never happen in the real west instead of the reel west.
Sierra Blanca could be near the location of the fictional ranch Spanish Bit in Duel in the Sun (1946). https://moviechat.org/tt0038499/Duel-in-the-Sun/5a11d43839d0810012ca0f0e/What-is-The-Fictional-Date-of-Duel-in-the-Sun