Q:

Is this character a Jedi?

Warning there are major spoilers in this question. Not all of them are hidden behind masked text blocks. Masking character name in title to avoid spoilers.
I'm wondering whether

 Rey

was a Jedi youngling from

 Luke's new Jedi Order which was torn apart by Kylo Ren.

The reasons for my suspicion include:
Her flashbacks. She has flashbacks which include screaming. She was witness or part of a traumatic event. It also appears to me as if she was dropped off on Jakku at a young age. Presumably this would have occurred immediately following the fall.
She is about the right age to have begun training as a youngling under Luke's New Order from birth. Though Luke obviously trained people who were not newborns, I expect he would see thevalue in training newborns especially if Yoda's force ghost was still advising him.
After her memories are triggered by Kylo Ren during his mind probe, she displays mastery of the force at a technical level, rather than something raw and untrained. There are three obvious examples:

She reverses Ren's mindprobe and draws information from Ren, himself a powerful force user who has been using mindprobes for a long time.

She uses force persuasion on a stormtrooper. More than that, she knows what force persuasion is and persists in trying to use it even though she initially fails (because through experience she knows she can do it).

She overpowers Kylo's attempt to force-pull Luke's lightsaber, grabbing it herself.

The only information I remember to the contrary is that prior to the mindprobe she clearly