The unaired pilot for Avatar: The Last Airbender was completed in 2003, but it was first shown publicly much later — in January 2005, just before the show aired in February. Nickelodeon didn't officially broadcast it, but they screened it at some industry events and with select audiences, and eventually it leaked online.
Timeline:
2003: The pilot is created as a pitch to Nickelodeon.
Early 2004: Nickelodeon greenlights the full show.
January 2005: The pilot is shown behind closed doors as part of early promotion — but not aired on TV.
February 2005: The actual show premieres with Episode 1: The Boy in the Iceberg.