Remember Avatar Roku’s temple in Season one, how the sun hit the statue on the Winter Solstice? Now compare the floor pattern and the door/sun opening mechanism in the Sun Warrior temple. They match.
On the Sun Warriors’ island Zuko tricks the door into opening, it was not yet time for it to do so. When Zuko and Aang do the dragon dance/imitate the ceremony, the egg rises, but since they’re too early, it does not hatch.
What this implies is: On the next solstice, when the sun hits the red gem and opens the door, the sun warriors will gather for the ceremonial dance. The egg will rise from the floor and the dragon will hatch.