The CDC website has the answer to this question-
https://www.cdc.gov/coronavirus/2019-ncov/travelers/testing-international-air-travelers.html
It is under "what types of tests are acceptable under this order?"
You must be tested with a viral test that could be either an antigen test or a nucleic acid amplification test (NAAT). Examples of available NAATs for SARS-CoV-2 include but are not restricted to reverse transcription polymerase chain reaction (RT-PCR), reverse transcription loop-mediated isothermal amplification (RT-LAMP), transcription-mediated amplification (TMA), nicking enzyme amplification reaction (NEAR), and helicase-dependent amplification (HDA). The test used must be authorized for use by the relevant national authority for the detection of SARS-CoV-2 in the country where the test is administered. A viral test conducted for U.S. Department of Defense (DOD) personnel, including DOD contractors, dependents, and other U.S. government employees, and tested by a DOD laboratory located in a foreign country also meets the requirements of the Order.
Most of the ones I saw for "international travel" in Germany run about 50 Euros-90 Euros and are RT PCR ones. Usually it will say it is somewhere when you go to book the test. But be sure it is really one of the ones listed since that is what we accept.
I used these guys (booked the International Travel) one specifically. Had it done on a Thursday, results by Friday night. Left Germany on Saturday. It was pretty convenient and there wasn't a line (though that was about 3 weeks ago now)-
https://covidzentrum.de/en/