I am an expert at getting BCs for my children. I have had seven UC homebirths. I have had seven live births. And I have seven legally registered BC from the state. AND I have had them in a total of five different states(Florida, Georgia, Texas, New Mexico, & Indiana).
The basic requirements that I have had to have were 1) my ID, 2) proof of my pregnancy, 3) proof of live birth (this is accomplished with a copy of a Dr's note from a well baby check up - must include baby's name and DOB), 4) and most of the time at least two witness statements (this is can be accomplished even if the person was not actually at the birth, however if there was anyone at the birth I would use them. I have my DH fill out a statement as well as two other people that basically states: "I personally know that (or I was a witness to the birth of) Sarah Jane Doe was born on January 2, 2007 at 3:30 pm. She weighted 6 pounds 6 ounces, was 21 inches long and was born alive." Then have them sign it along with writing in their complete name, address, and phone number, and dating it. I have been told that this is a legal statement. You can even have the have it notarized to make it a "legal document".)
Witness statements have been used instead of vax cards. Also, I have been asked for proof of residence (lease or utility bill) and once (in Georgia) I had to actually go to the court house and fill out an affidavit.
Most of the time the SS was issued with the BC, but on several occasions there was a mix up and I had to file for it separately. I just used the BC that I received from the state and then the same copy of a doctors note with baby's name and DOB. If they were not filed with the BC, I did have to go into a SS office and file in person, but I have never had any trouble. For each state, I just provided the same info for both the BC and the SS.
I have seven of each.