Once you've enrolled in classes and have some form of payment in processing (even if you're still waiting for your financial aid, it will show on your account), you can get your student ID made.
We start making IDs for each semester on the following dates:
Fall semester: August 1
Spring semester: December 1
Summer semester: May 1
I.e. if you register for and pay for summer classes on April 17, you still can't get an ID made until May 1. You can have an ID made at any point during a semester for which you are taking at lease one course (though sooner is better than later). You aren't required to have an ID on the first day of class, nor is there a penalty for getting one later in the semester.