I actually went to the infant care downstairs of my place. They taught us to put an earlier EDD but in the comments indicate the actual EDD. so the places with spaces can start to reach out to you. hope this helps! Otherwise is to visit your target places and leave your name on the waitlist.
It is not book early but placing your interest in the centre of your choice. You can go ECDA website to place your interest. The school give you call should there be availability.