“Third world” is Cold War framing, pitting the capitalist U.S. and allied countries (first world) against the USSR and allied countries (second world). The Third World referred to nonaligned Global South countries, which tended to be too crushed by the ongoing first world colonialism.
Denigrating the U.S. with implicit denigration to colonized countries based on its own colonialism feels a little off to us.
Could you provide a source for that claim?
SadArtemis already expanded on this well. Certainly Greco-Roman societies were well aware of Africa, even if not the extent of it. You might find Wikipedia’s early world maps page a good starting point.