Need newborn same day passport no birth certificate USA.

Hi. I’m planning on flying from Orlandowith my entire family including my newborn who will be about 3-4 weeks old to spend my postpartum in Europe with family. The whole same day agency seems really daunting. As I won’t have the birth certificate or ssn and they don’t have same day in Orlando only Miami. If my appt is the same day or day b4 will be cutting it close. Can I book an appointment the 14 day mark and buy my tickets after I secured an appointment? Nervous to buy 5 tickets without a for sure passport. Any advice? Thanks!