In 2016 I needed a passport relatively quickly (a few weeks maybe...I forget). I went to the office in Manhattan and they processed all my info, took my money and documents, and then told me that since I lived close to the Municipality where by birth certificate was (about 20 minutes from my house) that I needed to get a copy with my parents info and come back to Manhattan to finish the transaction.

However, they told me if I didn't live so close and/or my timeframe for needing it was sooner, they would have given me my passport with what I provided them.

That said, a lot could have changed since 2016...or maybe not.