First is excavation then carbon dating.
Archeologists use to uncover and unravel the ruins of ancient cities through carbon dating.
Radiocarbon dating (carbon dating or carbon-14 dating) is used to discern the artifact’s age by detecting the organic material by using the carbon isotope: C-14. The method is referencing on the idea that in radiocarbon is constantly produced in the atmosphere combining with sun’s cosmic rays and been found on plants animals. This originated from Willard Libby (1940) was awarded with Nobel Prize in 1960. The dating can detect up to 50 000 years ago.