The best way from Buenos Aires to Darwin is apparently via south Australia. Qantas flight QF14 “approached Australia from the south on Wednesday night, crossing the Great Australian Bight to then fly over the Red Centre to Darwin.” Traveller.com reports:
“The longest commercial flight in Qantas’ history landed in Darwin on Wednesday night after a route that took it from Buenos Aires over the coast of Antarctica on a near-18 hour long haul.
The repatriation flight was the return leg of a charter flight that carried Argentina’s rugby team home from Brisbane to Buenos Aires on Sunday after the 2021 Rugby Championship. The Department of Foreign Affairs were notified about the flight and worked with Qantas to use the returning plane to bring home Australians.
Flight QF14 took off from Buenos Aires at 12.44pm local time, 19 minutes behind schedule, but landed in Darwin five minutes early after a journey that took 17 hours, 25 minutes.”
With a view of Antarctica:
Captain Alex Passerini, Qantas’s chief technical pilot, said, “We’ll end up flying over the continent at around 73 or 74 south latitude, depending on the winds,” he said. “Hopefully the cloud cover will be kind to us and we can give our passengers a view.”
By comparison, in the north, 74 degrees north latitude crosses Novaya Zemlya in Siberia, here from Wikipedia: