On one hand you have folks calling TFA an ANH clone/rehash and on the other people want Rey to have the same path to the Force that Luke did. Not that these are all the same people, mind you. It's just an interesting thing to watch happen.
Rey has a history that most likely involves the Force in at least some respect. We are shown this fairly directly when she grabs Luke's lightsaber. Luke had no idea. Granted, it wasn't spelled out explicitly, but it didn't have to be to get the point across that she has some history there.
She is aware of the legends, the most recent and prominent of which were born a mere 30 years prior.
She is thus willing to accept her power, and as such displays early talent with it in different ways than Luke did. Training served to knock down Luke's barriers of disbelief. Rey has none. She has a natural head start thanks to the legends Luke left behind (and perhaps more,) but Luke had a bit of training. For ballparking something as ambiguous as the Force, I'd call that a wash.
She also had a freaking mind battle with a strong force user. This was the BEST thing that could have happened to her. A pure battle of will? Someone strong in the Force but untrained would conceivably learn a LOT from that battle about how, say, suggestion and domination works. Especially when you win, something that one ostensibly needs no training for since it's a raw, brute force battle. No surprise that her first overt use of the Force involved a Mind Trick.
To say that this wasn't obvious enough to the audience at large is a fair point, but one I disagree with as an audience member who immediately took the above away from Rey's use of JMT. Zero suspension of disbelief required.
Of course this issue doesn't exist in a vacuum. Kylo's weakness is oft-cited as the other factor contributing to "Rey feeling too powerful too quickly." This is a fair viewpoint that I don't share. It's really "what people wanted going in" vs "something different," and I like the different approach. Apples and oranges I suppose. Some folks wanted another all-powerful menace like Vader. Like ANH had. I am glad they went a diff route.
Kylo having his own journey and development is exciting. But even given that, he is already very potent and menacing. The final battle has been talked to death, but he basically took an otherwise lethal shot from a bowcaster, played around with Finn before almost killing him, and then owned Rey enough to attempt his main goal: bringing her to Snoke.
That Rey's belief in herself, years of actual melee combat experience, and the Force allowed her to catch a heinously-wounded, conflicted, frustrated Kylo at his not-best for a few moments and gain the advantage seems perfectly reasonable.
I feel like some people were watching the movie with Mary Sue detectors on and found exactly what they were looking for. This is not to say everyone with this criticism is guilty of such, but the very fact that this trope is such a prevalent talking point these days in general suggests that this probably happened at least a bit.