xD I think we're meant to assume that they used GFs throughout their SeeD training, even before the events shown in the game. After all, Squall starts the game with his own GFs, and we're told that SeeD get their strength from the GFs. Aside from the them, Selphie used the GF she found as a child, and Irvine hasn't used them enough to have memory issues.

I agree that it's a really contrived series of events, but it basically works out.