Summoned, not awakened. They awakened to the potential much earlier. It's like how the Persona 1 cast awakened to their Personas during the dream, but didn't summon them some time later. When all hell starts breaking loose. Or how the Persona 2 castbut largely didn't summon them until a little bit into the game.awoken to them as kids
The scenes we see in The Answer are when the casts awaken to their Personas, not when they summoned them. Fuuka awoken to hers during the game, so there was no need to show it to us again.
There are issues with Fuuka's character in P3, for sure. This isn't one of them tho.
Akihiko explicitly states that Fuuka has the potential, and she's also able to stay awake during the dark hour. That means she awoke to the potential shortly before being thrown into the Gekkoukan gym.
Regardless, the game never explains why she awakened to her Persona in the first place.