Schools/branches are not required to wait until the end of the application window before interviewing candidates and making offers. Some popular positions get many applicants within a couple of hours of the start of OPE. The interviews may start shortly, and sometimes offers are made on the spot.

To maximise your chances, you should apply as soon as possible to the positions that you want. You can always deliberate on whether to accept the offer later on. It doesn't hurt to go for more interviews, you learn something from every one of them even if you don't get offered/don't accept their offer. Good luck!