I am an American citizen and renewed my passport while here at home, in La Manzanilla, in April 2021. I made an online appointment for passport renewal in Guadalajara, went there with new passport photos, filled out application and whatever else was required. My new passport was Fedex-ed to me about 3 weeks after my appointment. If there are no appointment days or times available to meet your May expiration date, you can go to the Consulate early in the morning and request an emergency appointment. (I am not sure if you can request an emergency appointment online). Last year, this type of appointment was granted on the same day it was requested.

The procedure may have changed. Check out https://mx.usembassy.gov/passports/2996921