I dug up an old post I made over on the Canadian forum about this:
Possible explanations for Rey's rapid acquisition of the force (one or some combination of the following may apply):
1. Luke was a real biatch - "But I was going into Tosche Station to pick up some power converters!" Rey is not, as she's grown up fending for herself (yes, we have to suspend disbelief and ignore the realities of what happens to girls who are fending for themselves and not under the protection of adults; in real life she'd be groomed and passed around by Hutt pedophiles on planet Rotherham while the politically correct Republic's citizens dare not saying anything lest they be accused of Huttophobia, but I digress). So it's not inconceivable that a tough Rey, who already knows how to fight, can wield the force quicker than a limpdck like Luke, whose first crush was his own sister.
2. Luke's opponent was Darth Vader, who until the very end, had no inner conflicts, and was thus very strong in the dark side of the force. A biatch like Luke was never gonna beat a badass like Vader the first time around (here I'm referring to VADER of the original trilogy, not the prissy Anakin of Episodes 2 and 3). Rey's opponent, on the other hand, is a conflicted Marilyn Manson look-alike with regularly occurring premenstrual episodes, hence destroying First Order property on a regular basis (can you imagine Darth Vader having such hissy fits? I think not.). Not to be too hard on Ren, it must not have been easy having a father who was never around and was always off banging women in other star systems while being raised by effectively a single mother who was doing her best Ellen Ripley impersonation and leading a fight against the Empire. Tough Rey vs. prima donna Ren: Rey wins.
3. Rey may be Luke's child. While he was a biatch, he was also a Jedi knight. Legions of females of all species wanted to ride his lightsaber, so it's possible he has many spawn out there (and frankly, if there aren't, it's proof positive he's gay). And if she was Luke's child, it makes sense that she would be more powerful than Leia's child, Ren. Leia was sort of meh with the force, hence she never developed it.
4. Rey may be a child of the force, like Anakin. Remember Anakin's mother's immaculate conception story as told to Qui-Gon Jinn? Now it could be she didn't want to admit to a Corellian brandy fueled gang bang in the backroom of Mos Eisley with a group of Jedi knights passing through Tatooine, or it could be she was telling the truth, and the force conceived Vader. May be the same situation with Rey, which would explain why she quickly became powerful.