Some thoughts I had while watching the trailer for the umpteenth time:
1. According to the news that came out of the Star Wars Celebration panels, the desert planet, Jakku, is the sight of an old battle between the Empire and the Rebels/New Republic, and is littered with wrecked ships as a result.
2. Daisy Ridley's character is a scavenger on Jakku.
3. The two clips we see of the Millennium Falcon in the original teaser and the official trailer also show it on Jakku, engaged in a dogfight with TIE fighters and fleeing from a single fighter, respectively.
4. The official trailer also shows Daisy and John Boyega's characters running from a TIE fighter attack.
5. The clip of the Falcon shows it flying into the massive engines of a crashed ship--something a pilot, even one as daring as Han Solo, wouldn't be reckless enough to do (especially with a ship the size of the Falcon) unless he was familiar enough with the lay of the land--as Daisy is.
6. The two interior shots of the Falcon show BB-8 peeking around a door and, later, Han commenting to Chewbacca that they're "home."
So it's probably safe to assume that the Falcon was damaged in the Battle of Jakku and abandoned, and was later found by Daisy's character, who managed to fix it up and get it in working condition (as much as can be expected) by the time John Boyega's character comes along and they're forced to flee from the Imperial forces that are chasing after him--meaning Han and Chewie don't step foot on the ship until much later in the movie.
That's probably been obvious to everyone else from the beginning, but hey, I thought it was a cool idea. I bet I'm right, too. And how great would it be to see Daisy's character scrounging for parts on Jakku, then walking into a makeshift spaceship hanger where an aged and battered, but still beautiful, Millennium Falcon is sitting there waiting for action?