Seems like they make sure we do not see who is dragging Rey along but still provide a clue with a long shot of the spaceship in the distance. I don't think we ever get an external view of the Erevana, the freighter Han is using after having to abandon the Falcon. Could it be the Han dropped Luke and Rey on Jakku and somehow had to leave the Falcon behind?
We don't have any canon information on who left Rey on Jakku.
But most certainly, Han didn't "leave" Falcon behind there:
“Look.” Taking a chance, Rey lowered her hands so she could spread her arms wide. “I don’t know all the details for sure. I’m not privy to Plutt’s private accounting. But talk says that Plutt stole this ship from the Irving Boys, who stole it from Ducain.”
“Who stole it from me!”
(Alan Dean Foster's novelization)
I don't think it was that big. (The Evana is 6 or 7 times bigger than the Falcon, at least.) I thought it looked more like a T-47 airspeeder more than anything else: https://i.ytimg.com/vi/XLu-blZVTUs/maxresdefault.jpg but those are atmosphere-only craft, so what do I know.