Is there any evidence in the ancient Sources that the Talmudic rabbis were aware of the existence of America?
There are no sources which speak of the Americas. At best the Zohar (not an ancient source) maybe attributes one or two continents out of the seven but there is no indication that any of these refer to the Americas.
In any event, the rabbis put their emphasis on Halacha. They were honest to admit that most of their knowledge about astronomy derived from the pagan Greeks. I do not think the rabbis were even aware that the earth was spherical, much less about a new continent.
Anyways there’d be no practical reason to know of its existence. The Catholic Church disputes’ with Columbus weren’t centered around the shape of the earth. They refused to fund Columbus because they didn’t think they’d be a new continent. And the only reason they left Europe was for trade. A practical reason.
At best we can say the rabbis might have known something about the earth from the Greeks but were ignorant in what new continents lay ahead.
 According to the media news outlet CNN Christopher Columbus may have been part Jewish.
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