One of the radioactive elements to test for is Cesium 137,
This radionuclide has a half life of 30.2 years and is one of several unique byproducts of nuclear fission or atomic detonations. It is present in all authentic Trinitite specimens.
All radioactive elements have a half life. The radioactive elements produced by the Trinity Test on 16 July 1945 are also well know. To increase the confidence of testing, the amount of each radionuclide in each sample would need to be detected and compared with the expected amount that would be in true Trinitite given the elapsed time since 16 July 1945.
If the specimens have a report from testing laboratory, get a copy of the report and verify it with the laboratory. Ideally, such reports should had a picture of the sample that was tested. If so, ensure it matches what is being offered for sale.