1862-invention of the Gatling gun.
Before the invention of this weapon, the Plains and Pampas nations could go toe to toe with European-style armies and win. But the creation of rapid-fire guns doomed them militarily.
I wouldn't even argue this, particularly, is a major turning point. The Texans, later Americans, could contest the Comanche and others with assistance of Native Scouts and after adopting native tactics, raid native camps, etc. While a standard infantry army was run around in circles, and there wasn't much of the way in Cavalry in the Old West, the Rangers did well enough, though the first rangers (back in the 1830s, if I recall correctly) had to be recalled to teach the newer rangers who were reinstated a few decades later.
If there's a better turning point/new weapon that changes the calculus, it isn't the Gatling gun, it's the creation of the Colt Single Action Army revolver, if you want to pick a single firearm that gave settlers a major advantage over the natives. Moreover, it allowed them to operate in the saddle and exchange fire directly instead of being forced to dismount to fire.
And it isn't to say they could have defeated a European Style Army in a straight-on battle and guaranteed a win (though they could certainly perform well enough to route unsupported infantry); most of the Comanche victories were against military outposts that were not expecting battle and against townships, and then it consisted mainly of Cavalry vs infantry without their own cavalry support, field artillery, etc. They attempted not to put themselves against a field army in preparation for battle (I can't think of one in the time period until the examples in the late 19th century, with Custer's defeat being a notable one).
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As to the OP, one thing that might help some of the natives remain in their original homelands would be the Indian Removal Act not passing - it only made it through Congress 101-97, with 11 not voting. You only need 2 voters to flip and one that didn't vote to say nay to make the act fail (or some other combination thereof). It wouldn't necessarily result in a good ending (what would the Georgians do in reaction to being told the Cherokee et al still maintain their sovereignty by the Congress
and the Supreme Court), but it would uphold Cherokee sovereignty... though the question is for how long.