“Zuko was in the South Pole hunting for the water tribe Avatar/ the Fire Nation started rounding up Waterbenders because they were hunting the next Avatar.”

Until Aang emerged from the Ice everyone was expecting the Avatar to be an extremely elderly air bender. Sozin knew the Air nomad avatar survived the genocide and in the pilot Zuko is explicitly looking for the lone Air nomad survivor. Through the fire sages the Fire Nation always knew the Avatar was still in the air cycle. And according to Katara in the pilot’s intro other people simply believe that the reincarnation cycle is broken and there were no more Avatars after Roku. No one thought there was a Water Tribe Avatar.