I think legally the public school you're assigned to would have to accept your daughter for enrollment whenever you bring her to register. But it will be much much better for your daughter if you enroll her before the first day. This is true for a few reasons:
First, in the days and weeks before school starts, the principal and staff will be working on making class lists and assigning each child to a teacher. If they know your daughter will be there, they'll be able to assign her to the teacher and class she's best suited for, rather than just sticking her in whatever class has space available if you enroll on the first day. Also, you'll be required to provide a number of documents to the school for enrollment (immunization records, proof of residency, etc). It would be too bad if you got turned away on the first day because you were missing one of those documents. Safer to start the process as early in advance as possible so you're sure your daughter is allowed to attend on the first day.
Second, the teachers will do a lot of preparation work to make the kids feel comfortable in the class. They'll put up name tags in several places around the class (desks, cubbies, coat hooks, class rug, text books, etc.) If you came on the first day, you couldn't expect the teacher to create all of those things for your daughter and she may end up feeling really left out.
So, while it may be possible to enroll your daughter on the first day, it will be a lot less stressful for you, your daughter, and the school staff if you do so a little sooner.