The eight year old rugrat in the first prequel was quite remarkable without any training. We have new evil force users, despite the requisite "always being two, a master and an apprentice" both dying at Endor. Luke spent a trivial amount of time training with Yoda and Kenobi, most of which was spent convincing the farmboy that it was a simple matter of "just doing" the impossible.
As far as we know, the rigors of Jedi training in the Old Republic were intended to prevent people from misusing "what comes naturally" and falling to the dark side. That Luke, who didn't benefit from that training, had students who fell to become "Knights of Ren" reinforces that line of thinking.
If we don't know what the training is for, we can't judge if/how Rey is remarkable compared to other Force users. Regardless, given how the movie ends, it seems likely that we'll have illumination on these questions.
Wait, I must be thinking of a different film, nevermind.