The Native American vs. Greeks/Romans/Egyptians | AskHistorians Archive Observer

As in most cases with history, the answer is in asking who is writing the history and what kind of bias they have. You glance off the answer here when you ask:

Is it as simple as history looking at the height of those civilizations while we look at the time of conquest of the America's?

History isn't just a collection of facts, it is the assemblage of those facts into a coherent narrative. As such, where you start and stop your narrative and what elements of it you choose to highlight or focus on are going to significantly change the tone and message of the story you are telling.

In terms of "savage" Native Americans and "civilized" Mediterranean people, these concerns are absolutely at play. Primarily, we have to think about how the history (and ethnography) written in the 19th and early 20th century has colored our perception of these different groups.

Note that in this case, all of the groups you named specifically (Sioux, Navajo, and Apache) were targets of the U.S. military in the 19th and 20th century. These groups were targeted for displacement, assimilation, and genocide in order to aid westwards imperialism by the U.S. It was helpful to then emphasize the "savagery" of these people as justification for the "civilizing" mission U.S. imperialism. This was known in a British context as the "White Man's Burden", but the idea is the same across the board when we talk about European colonialism in the 17th to 20th centuries. Writing your own history as one of "civilization", and the history of the "other" and the target of your colonial ambitions as one of "savagery" justifies those people as targets. I discuss this aspect of European colonialism at greater length in this post.

In short, the very definitions of "savage" and "civilized" where established by 19th century anthropologists and historians by putting contemporary European societies at the center of the definition for "civilization", and anything dissimilar as "savage". Rome, Egypt, Greece, etc., where folded into this narrative of civilization after the fact in order to explain why contemporary Europe was civilized (i.e. it had a "civilized" past where Egypt begat Greece begat Rome, etc.) and other societies were savage because they lacked this.

You can see some of this in action by looking at portrayals of different Native American societies. Native American groups which lived outside the control of European colonial powers (including the U.S.) were generally portrayed much more unfavorably as "warlike" and "savage", while (usually sedentary, agricultural) groups under colonial control where thought of as more civilized. I discuss this dichotomy at length in this post, though I should stress this isn't an ironclad rule. It's a trend, but not an absolute one.

I won't fully address your last question since we don't really do hypotheticals in history and anthropology, but I can say that perhaps the premise of the question isn't totally sound. I discuss that issue at length in this post.