No. You need a valid passport to re enter the USA. Also, applying for a U.S. passport outside the United States is different than applying inside the United States.
You must apply in person at a U.S. embassy or consulate. Each U.S. embassy and consulate has different procedures for submitting and processing your final documents, but the forms, supporting documentation, fees, and finished products are the same.
For locations https://www.usembassy.gov/
For requirements https://travel.state.gov/content/travel/en/passports/apply-renew-passport/outside-us.html
Expedited processing is not available when you apply outside the United States. In an emergency, embassies or consulates can issue limited-validity passports.