When Rey was left on Jakku, she faintly remembers seeing a starship leave Jakku.
We're given a little glimpse of the Starship in Star Wars: The Force Awakens.
Who owned that Starship?
As in, was it a First Order / Empire Starship or a "good guys" Starship?
Obviously this would be a huge clue into who left her there (maybe), but I do understand that there may not be an answer for it at this time.