The evidence used to obtain your social security card should be sufficient for any DMV office.
Religious record made before the age of 5 showing your date of birth;
U.S. hospital record of your birth; or
You may want to obtain a US passport to prove you are a citizen. It is usually sufficient proof of status for educational purposes. Consult the link for acceptable forms of primary and secondary identification for passport issuance purposes. You do not necessarily need a birth certificate if you can present other acceptable forms of ID.
This is general information and not legal advice and no attorney client relationship is created.
You can either get proof of your citizenship through the Immigration Agency, but filing for a certificate of citizenship, or you can apply for a U.S. passport through the Department of State. There are ways to prove your birth in the U.S. without a registered birth certificate. For example, affidavits from people who were present at your birth can also be acceptable with other proof. I would suggest hiring an attorney for help with the process.