The Date.

In the opening narration James Aherne Jr. aka War Bonnet, says that he was 11 years old in 1868. If he was 11 during any part of 1868 his 11th or 12th birthday would have happened during 1868.

Since he is seen traveling in warm weather during the 1868 scenes, and thus about March to October 1868, one might suppose that he turned 12 sometime after March 1,1868 and thus was born sometime after March 1, 1856, and that he turned 11 sometime before October 31, 1868 and thus was born sometime before October 31, 1857, and thus was born between about March 1, 1856 and October 31, 1857.

So Aherne/War Bonnet would have been about 19 or 20, plenty old enough for a Sioux to fight, when the Great Sioux War started in 1876

Since Charlton Heston was born October 4, 1923, and since The Savage was released in September 1852, Aherne/War Bonnet would have been about 29 years old in the main part of the film if he was as old as Charlton Heston was when The Savage was released, and thus the main part of The Savage might happen about 1885-1886. But an adult fictional character like Aherne/War Bonnet can be imagined to be 5 or even 10 years older or younger than their actor, so the main part of the Savage could happen about 1880-1891, or even about 1875-1896.

At one point Corporal Martin says that he's been in the army for 20 years (or over 20 years) since the Civil War (1861-65), thus putting The Savage about 1881-1885; or maybe he says since Grant marched to Richmond (1864-65) thus putting The Savage about 1884-1885 - or later if he said over 20 years.

And of course that doesn't make historical sense. In real history, there was an uneasy and often violated peace with all the Teton Sioux from 1868 to 1876, then the non reservation Sioux were defeated in the Great Sioux War of 1876-77, went to the reservations, and ended their old lifestyle. The whole plot of The Savage was impossible after 1876-1877.

So if there is any way to interpret Corporal Martin's words differently than the above interpretation, the war in The Savage could start in 1876 and be part of the Great Sioux War.

Or maybe The Savage simply happens in the wild west of imagination. Western movies often depicted war with a tribe when there was peace, or peace with a tribe when there was war, and rearranged the geography of the west to suit the plot.