The central justification for America isn't the argument for life, liberty and the pursuit of happiness. It's the argument that America is a place of refuge, a nation of immigrants, a place to remake lives: and that this idea matters even more than the ancestral rights of the continents' original inhabitants.
Even this is not a strong argument.
But if you take this away, assume it's about establishing a white man's homeland, colonisation and immigration are merely invasion of territory which rightfully belongs to its original inhabitants.
Send one home, send them all.