Rey is Ezra and Sabine's daughter.
I thought they were finally going to explore the romantic angle when they sequestered the two, but the rest of the group immediately rejoined them. There's not enough time before their resolution, now, but it works for a number of reasons. The major rule of supposition it breaks is that Rey is a Skywalker. After all, at its heart, Star Wars is really nothing more than a soap opera about the Skywalkers in the same way that the Godfather movies were a soap opera about the Corleones. Furthermore, "Rey" also means "King" in Spanish, indicating royalty, which would seem to be an allusion to her genealogy (i.e. Princess Leia).
But it makes sense of why Rey was left by her parents. Rey and Sabine conceive her, then leave her as a young child to go die in a side of the Yavin fight (the first Death Star explosion) we never saw before that makes the miraculous victory understandably more explainable.
The reason it doesn't work is that Rey is too young. In her vision in The Force Awakens, when the ship flies off to leave her, she's already a young girl that looks to be between 4-6 years of age. The film takes place in 34 ABY (34 years after the Battle of Yavin when the first Death Star is destroyed, and during which the original film is set). So for that to be her before the Death Star would make her roughly 40 years old.
Nevertheless, the notion that Ezra and Sabine could reproduce a force-sensitive child is a very exciting idea.