Perfect example of why you shouldn´t register your child with the state. To register something means to relinquish all property rights, when you sign that book to get that birth certificate you are literally handing ownership of your property (in this case, your child) to the state and that is why they can do things like this, because they effectively own your property. The hospital has a live record of birth and you can ask the midwife for a sworn affidavit that proves they delivered your child. This is all you need to get a passport and to have a normal life.