while u can make a case that what the european powers did in what is now the united states was continued by the usa its insane to say that it is the same event as what other or the same european powers did elsewhere some of these genocides are separated by centuries they were carried by different people often from different countries using different tactics for different reasons to completely different people who were not in contact with eachother and they often did this without even known what other colonizers were doing, the idea that what the european powers were doing was somehow cohesive is ridiculous.
i think ur scale of time is way out of whack for this, for example the peoples of the caribbean had already been complety erased for decades before jamestown had been stablished let alone the colonies let alone an american national identity.
And also the original meme about the united states not the entirety of the americas it was about what the united states did which israel and nazi germany copied.