The necessity of genocide was the operative, working assumption of the expanding American nation. "Manifest Destiny" was born at Plymouth Rock and Jamestown, later to fall (to paraphrase Malcolm) like a rock on Mexico, the Philippines, Haiti, Nicaragua, etc. Little children were taught that the American project was inherently good, Godly, and that those who got in the way were "evil-doers" or just plain subhuman, to be gloriously eliminated. The lie is central to white American identity, embraced by waves of European settlers who never saw a red person.
The "criminal intent" is why we can say Euro-Americans are guilty of genocide even though most Natives died from disease. If you intend to commit a legal or moral crime and people die while you're committing it, you're generally guilty of some kind of murder.
As for the tired issue of whether we can judge centuries-old invaders by "our standards," that debate is over and my side won it. See Those Evil European Invaders for details.
For more on the subject, see The 4th of You Lie.
Below: "We didn't call ourselves conquistadors because we loved peace and harmony."