I don't know about Logic Express, but certainly in Logic Pro (and in a fair few other Mac apps) that there doesn't need to be a window for the app to be running - as you point out, the presences of the toolbar shows you this.
To open a window (in Pro at least, so I assume it is the same in Express) go to the Windows menu and choose the type of window you want to see - probably the Arrange window is the one you are expecting.