The parent - teacher meeting ___________ be as early as next week.

 Here, might is the correct option as it is used to indicate the possibility that something is true or will happen in the future. Would is used to express the sense of will in reported speech or when referring to an event that has not happened yet. Must is a modal verb indicating that somebody is compelled to do something because of a rule or law, or that is necessary or advisable to do something. Will is used to indicate future time, polite questions or requests etc.