The majority of tests do fall under a NAAT or Viral Antigen test, including rapid viral antigen tests and many at-home tests shipped overnight to labs. Many popular locations in Mexico and the Caribbean have started to offer testing at the airports on departure from rapid antigen test results to continue facilitating international travel to the USA.
Alternatively, there is usually availability for COVID testing to promptly be done at most international locations, generally with results back in about 24 hours. It is a good idea to check with local labs that provide testing to make an appointment to ensure timely results.
There are some exemptions to the requirement for a negative test.
The first is if the passenger has tested positive for the virus in the last three months before departing back to the USA. In this case, they will need a copy of the positive test results taken within the previous 90 days before traveling back to the USA. They would also need a signed letter on official letterhead that contains the name, address, and phone number of a licensed healthcare provider or public health official stating that the passenger has been cleared for travel.
The testing requirements are the same for a negative test except that it would need to show a positive result.