Yes, it's also possible she'd been to Edinburgh to see some of the festival, to visit a friend, for a job interview...
She really could be from nearly anywhere, may be a student or recent student in Manchester, Bolton, Salford, Edinburgh - though if she's meant to be attending any college or University now I'd have expected her to be reported missing to police already as the Unis have been in session for about a month. As students often attend Unis a long way from where their parents live, that wouldn't give a clue where she's from.
If she wasn't a student it's more likely she is either local to where she was found or is from Scotland.
The police seem to have no idea who she might be unless they are withholding some information for now.