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No, in order to enter Mexico or the US by air, both you and your child will need a passport.
If you are US citizens, you may be able to get a passport in a hurry at the San Diego Passport Agency; be sure to follow all the instructions on their page regarding appointment scheduling and necessary documentation for both you and your child.
If you are Mexican ...
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If you were vaccinated in New York, you can get an Excelsior Pass.
What is Excelsior Pass?
Excelsior Pass provides secure, digital proof of COVID-19 vaccination or negative test results.
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