Pretty much soon after the birth, as long as it is done before 42 days (6 wks).
I think it varies from Country and States, Link attached has some procedures and contact numbers with whom you can clarify.
Though hospitals may keep a record of the birth they do not keep birth certificates.
I was born at home . The Doctor arrived afterwards. He later died and filed no record . How do I obtain a passport without a birth certificate ?
The information on original birth records is not changed. A change of name would be filed in a court of jurisdiction.
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2 weeks
The authorized birth certificate may refer to the Original birth certificate rather than the Copy of the Birth Certificate.
The "long certificate" proves that Barack Obama was born in the US.
Not all states have long/short forms, but you do need a passport and to get that you have to have a birth certificate. As long as it is from the state where you were born it doesn't matter the length of the form.
The answer can be found under the same question " Is Obama's Purported Long Form Birth Certificate a Fraud?" with capitals except in the word "a".
Lucas Smith affidavit, containing Obama's Kenyan birth certificate and represented by Dr. Orly Taitz, filed with U.S. District Court in Southern California; Judge David O. Carter to look at.
Why would you want to sign a birth certificate?
When a person dies.
You should be fine as long as you have your birth certificate and the rest of the requirements