I think she got possessed by using a ouija board. I honestly don't know how an excavation of a vulgar demon statue could possess a girl in a different county, unless by being earthed, the spirit was free to roam the astral plane via ouija boards? It's been awhile since I've seen the movie and read the novel.
If you follow the complete story you find that Regan was chosen to be a vessel and the Ouija board was just the doorway which Bulzuzu chose to use. Father Marin had been fighting this demon since he was a young man and the demon statue represented the battle he had been waging for years.