H1B VISA expiring June Mid & daughter born in US does not have US passport

Hello !!

I am on my 6th year of H1B which is ending on June mid 2020. My daughter was born in US this year on January 2020. I applied for her passport on March mid. Due to COVID-19 situation, I have not received her passport. I reached out to the US passport center & they told all the centers are currently closed & it may take several months to get my daughter’s passport. I checked if I can pay extra to expedite the application, they confirmed at this moment everything is stopped & I need to wait.

As my H1B is expiring on mid June 2020, I cannot travel back to India without my daughter who will be 4 months. Is there a way I can legally extend my stay in US until I get the passport or is there a way to travel back to India with just her birth certificate?