I am certainly not an expert in this field and won’t pretend to be. In graduate school I took a wonderful class on socio-linguistics (and this was back in the 70s, so knowledge and theories have changed, I’m sure). We learned in that class that words come into existence only when there is a need for them (and the term “need” can be loosely defined here). The need might be simply because a group may have never encountered this “thing” before, and therefore it should have a name so one can communicate to others about it. It may require a name because of some social or political “need.” And new words can be created to catch attention, to stand out from the crowd or just because someone has an interest.
In simpler societies, terms are typically created out of necessity, to name a new object or fit an immediate cultural need. If objects could easily be lumped into one category without difficulty, they were. Correct me if this is wrong (and it might be), but we were taught that the term “maize” initially referred to a wide variety of domesticared grains, rather than just to the one we now call “corn.”
My guess is that the natives of the continents we now call North and South America approached this situation differently, depending upon their social and political approaches to others. Those groups (tribes, families, clans, societies, etc.) who were focused upon establishing settlements and staying there probably had no clear name for a continent, because they had no need to know that there was such a huge land mass under their feet. They had their homes and were part of the land, and they may have had a name for their immediate surroundings and adjacent areas.
Those groups who were nomadic may have had terms for the larger land area because they travelled to different locations to have their needs met. Those groups who were warring peoples, seeking to overtake other settlements, steal belongings from others and increase their gene pool by taking women and children from other groups into their own ranks, may have had words to the larger land mass. Those groups especially who had an interest in conquering and adding to their empires probably had the most interest in naming the land areas, although they may not have a name for an entire land mass (unless it ALL belonged to King Whateverhisnamewas).
A land mass itself usually has less importance than the political forces active within it. For example, the term Europe (or Europa) has been in use for centuries. But in and of itself it was a less useful term than understanding the political boundaries within it, such as “The Holy Roman Empire.” On our side of the ocean, living in North America has less meaning to me than living in the United States, although I know both are true. In addition, knowing that I live in the southwest US, in Arizona and in Phoenix all have special meanings to me, over and above being a US citizen.
Which brings up something of a pet peeve for me (sorry for detour here). In the USA, we call ourselves “Americans,” which is a technically true term. But this word does not denote us as US citizens. Canada residents can call themselves Canadians, Mexican citizens can call themselves Mexicans. Do we call ourselves “Statians?” “United Statians?” “Usalians?” ( Personally, I like that last one.)