I agree. The force is in her already, but she rejects it in the beginning of the film. The “awakening” is Rey choosing the force, and taking up the role of the hero.

Off topic edit suggestion: add Anakin’s theme to the reunion scene at the end of the film. Originally, Yoda’s theme and Luke/Leia’s theme plays for seemingly no reason. But with the force ghost climax, it makes sense as the spirits of the Jedi live in Rey. Adding Anakin’s theme would support this and allow for some more prequel music in this movie, tying all the film’s together a little better.