You do not need a passport to enter the US when you have a Green Card.
See https://www.uscis.gov/green-card/after-green-card-granted/international-travel-permanent-resident for the official text:
What documents do I need to present to reenter the United States?
If seeking to enter the United States after temporary travel abroad,
you will need to present a valid, unexpired “green card” (Form I-551,
Permanent Resident Card). When arriving at a port of entry, a U.S.
Customs and Border Protection Officer will review your permanent
resident card and any other identity documents you present, such as a
passport, foreign national I.D. card or U.S. Driver’s License, and
determine if you can enter the United States. For information
pertaining to entry into the United States, see U.S. Customs and
Border Protection’s webpage.
It says 'or US Driver's license', so it will be good enough in combination with the Green Card.
From own experience, I have multiple times travelled to Europe and back to the US, only needing the destination country's local ID card and the Green Card. Although they typically ask for your passport, it is ok to not have one.