Does the quiz have a time-limit? If so, it will have been submitted that amount of time after the students started.
Also, just because the quiz settings do not currently show a close date, there could have been one in the past, and then the settings were later altered (once the teacher realised the problem with the settings they had originally).
The only other place there might be a time-limit or close date is under Quiz admininstration -> User/Group overrides.