The idea that as victors, the treaties you entered into with the opposing side are somehow not meant to be upheld is not a righteous notion. The US' repeated violation of promises made to the various first nations is a detestable part of our nation's history. That modern jurisprudence has starting to uphold treaties our country entered into and never formally revoked is a good thing. A nation should be its word, not merely a bludgeon.
Second, what do you think winning a war means?
It's not always -- usually? almost never? -- a matter of one side eliminating or crushing the other to the point of abject subjugation. Rather, once there's a clear "winner", the losing side is usually willing to accept a unfavorable treaty that gives the victor whatever land or trade benefits they were after, and in return for the losing side not saying "fuck it" and trying to take as many people as possible with them, the winning side generally agrees to leave existing power structures largely intact and leave them some part of what's theirs.
If you decide they're going to live then yes. You need to show them that if they can't or won't unconditionally surrender and change their ways then they will in fact be abjectly subjugated and their lives will be miserable. Eventually enough of them will agree that it's not worth it. That was more or less the the USA approach with Japan in WW2. The thought being that they will fight to the death if they feel there's any sliver of hope. So nukes were dropped which showed there was not and that it wasn't worth fighting anymore.
The other option is to just slaughter them. This has been used more frequently throughout history.
After the atomic bombings -- and the Soviet advance -- Japan accepted these conditions, unconditionally, instead of holding out for better terms, like retaining conquered territory.
(Edit: Now, if you want unconditional surrender, the German Instrument of Surrender, now there's an unconditional surrender.)
https://www.supremecourt.gov/opinions/19pdf/18-9526_9okb.pdf
JUSTICE GORSUCH delivered the opinion of the Court.
On the far end of the Trail of Tears was a promise. Forced to leave their ancestral lands in Georgia and Alabama, the Creek Nation received assurances that their new lands in the West would be secure forever. In exchange for ceding “all their land, East of the Mississippi river,” the U. S. government agreed by treaty that “[t]he Creek country west of the Mississippi shall be solemnly guarantied to the Creek Indians.” Treaty With the Creeks, Arts. I, XIV, Mar. 24, 1832, 7 Stat. 366, 368 (1832 Treaty). Both parties settled on boundary lines for a new and “permanent home to the whole Creek nation,” located in what is now Oklahoma. Treaty With the Creeks, preamble, Feb. 14, 1833, 7 Stat. 418 (1833 Treaty). The government further promised that “[no] State or Territory [shall] ever have a right to pass laws for the government of such Indians, but they shall be allowed to govern themselves.” 1832 Treaty, Art. XIV, 7 Stat. 368.
The current government tend towards ‘truth and reconciliation’ is an attempt (or at least a gesture) to investigate and rectify these wrongs and treaty violations.
I’m sure the same holds in the US in areas where there was not a wholesale genocide.
I only say that to caution advocating for other countries to adopt the approach Canada has taken. I am of the view there were a lot of classic examples of well intentioned policies with disastrous results.
At the same time, I don’t know enough about the issue to offer alternative policy without worrying about the sensitivity of the issue.
The logic of ‘conquest->hegemony’ does not quite work in parts of North America because the ‘conquest’ was not a traditional one, but rather because of duplicity and breaking treaties, which- in a rules based order- typically have methods of restitution.
Parts of the USA, like the Russian conquest of Eurasia, were traditional conquests where the invaders drove out the inhabitants by force, but that is not a universal narrative in the European colonization of North America.