It has already been demonstrated that Force abilities and proficiencies manifest in people before any Jedi training. What does most Jedi instruction consist of? Clear your mind. Focus. Do or do not, there is no try. I am not sure what other instruction would be involved in levitating a rock.

Luke was very unfocused. He was sheltered by his aunt and uncle and was not very self reliant. Rey is none of those things. She is very focused and extremely self reliant. She is confident and believes in herself.

No training can teach you a mind trick as well a having Kylo browse through her mind. Also when we see her use the Force, she is in distress, not swinging a lightsaber at a practice droid. People often exceed expectations in extreme situations.

A lot of the Jedi training also appears to be their philosophy. They attempt to mold people with Force abilities into their ways. Rey is a scavenger. She takes what she can use and leaves the rest. That might not sit well with some, but I have no problem with her making her own way. I love it actually.

I have no idea where they are going to go next with these new characters, but I can’t wait too see it.