Is there a minimum amount of time an employee must be under the direction of a supervisor before that supervisor can rate that employee?

YES, if the employee is new to the company it may take up to three months to rate the employee as in the initial month or so the employee goes through orientation and training  and then starts working on his own.

Yes absolutely. Unless the supervisor has spent considerable time with the employee it is neither possible nor fair to rate the employee. However mere spending time with the employee is not enough, the supervisor should spend on job quality time with the employee. 

Every organization has a strong onboarding process. Some of the organization also have very strong pre onboarding process. The onboarding process should ensure that an employee should be aligned to the goals for the role s/he is going to essay in the organization. A supervisor;s role is to have a continous dialogue with his direct report so that any challenges or issues faced by the employee in performing the role is addressed immediately. Thus it is not about the time spent with a supervisor but the ability of the supervisor to ensure that the employee is productive at the earliest . Thus rating becomes an outcome of the performance of the employee under the guidance of the supervisor.