usa – U.S. and Mexican citizen flying from U.S. to Mexico

I already applied to get my US passport but I don’t think it will be ready on time, I’m also a Mexican citizen, so, if I’m planning to fly from San Diego to Mexico City, can I do it with a Mexican passport? I also have a current green card that would probably work for the way back. I need to know as soon as possible, otherwise, I’ll need to cancel my flight.