I know that a round earth was a generally accepted belief around the time of Columbus (contrary to a common misconception). Are there globes that were made sans America? Or was that later invention?
Yep, globes existed -- which shouldn't be surprising because the sphericity of the earth was known well before Columbus (who didn't confirm this, by the way -- Magellan's expedition was the first to circumnavigate the Earth.) There's a surviving globe made by Martin Behaim that dates to 1492, before Columbus returned from his voyage, which has a blank spot (well, it's ocean and islands) where the Americas should have been.
I've actually written before about the non-elite understanding of a spherical earth before Columbus; these links might be of interest to you.