Is there any evidence in the ancient Sources that the Talmudic rabbis were aware of the existence of America?
although i dont know if the sages of the talmud knew about america, i assume they did, because adam harishon did know about it. ''every land upon which adam decreed settlement was settled; every land upon which adam did not decree about was not settled'' [berachos 31b] how would they know this if they didn't hear about america
Most rabbis put their emphasis on Halacha. But they were honest to admit that most of their knowledge about astronomy came from the Greeks. I do not think the rabbis were aware that the earth was spherical or that the earth rotated around the sun, as Rabbi Slifkin demonstrated in his books, much less about the Americas.