Warbler said:
You don’t just become a Jedi without training.
She may be a nobody who has a strong feel of the Force. There isn’t any indication she has a desire to become a Jedi. She says specifically that she’s there to find out what her role is in the story she saw in her flashback.
Luke also makes a point of informing her that the Jedi don’t have some sort of special right to the Force. Hopefully she’s Rey Random on all levels. No familial connection, no faded robe hoodie Jedi. We’ve had 40 years of that.