A birth certificate is not one of the documents required for an N-400 application for naturalization.
Scott D. Pollock
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USCIS needs proof of your identity. If you have your passport from your native country and your green card, then you should have sufficient documentation. Additionally, in your alien file, there should be a copy of your birth certificate (as it was likely submitted during your application to adjust status).
That said, I'd err on the side of caution and retain counsel to handle the filing for you and attend the interview with you.