The short answer is no.
Travel to Mexico by land or sea without a passport is possible if you have a Passport Card , (or other Western Hemisphere Travel Initiative document) but unfortunately travel on a passport card explicitly excludes international air travel.
From the WHTI site -
WHTI document requirements for air travel went into effect in January
2007. All U.S. citizens and nonimmigrant aliens from Canada, Bermuda, and Mexico departing from or entering the United States from within
the Western Hemisphere at air ports of entry are required to present a
valid passport (or NEXUS card, if utilizing a NEXUS kiosk when
departing from a designated Canadian airport).
For land travel, it says that under 16s that are US citizens can enter the USA with just a birth certificate, but I'm not sure if this applies to entering Mexico!
U.S. and Canadian citizens under age 16 may present only proof of citizenship, such as a birth certificate or Naturalization Certificate.
Mexico appears to have additional requirements (spanish-only) for entry for unaccompanied minors, in any case.