Yes look on the web page they give you (www.ssa.gov) all documents for obtaining ss card are posted. Most definitely make sure you have you government ID and if you have a medical card with your name on it they give you a receipt with ss number on it until you get the new one in the mail. Then the card takes about 7 days for you to receive. That is quick compared to other places you can get your ss card from.
If I recall correctly, the SSA requires multiple documents, so you'll probably need more than your birth certificate. Google "social security card requirements" -- the SSA website should be at the top of the list.
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