As I remember, the Babylonian sequence of the movie Intolerance (1916) describes Prince Belshazzar in charge at Babylon while King Nabonidus is away doing archeological excavations. I think that the title cards used the word archaeology or archaeological.
From Wikipedia, Nabonidus (who reigned from 556–539 BC):
Nabonidus is known as the first archaeologist. Not only did he lead the first excavations which were to find the foundation deposits of the temples of Šamaš the sun god, the warrior goddess Anunitu (both located in Sippar), and the sanctuary that Naram-Sin built to the moon god, located in Harran, but he also had them restored to their former glory. He was also the first to date an archaeological artifact in his attempt to date Naram-Sin's temple during his search for it. Even though his estimate was inaccurate by about 1,500 years, it was still a very good one considering the lack of accurate dating technology at the time.
I am sure there are experts on the history of archaeology who have opinions on how much Nabonodus's activities should count as "the worlds first archaeological work".
But until someone gives strong evidence that there was archaeology before Nabonidus, or that what Nabondidus didn't wasn't really archaeology, we might as well accept that Nabonidus "initiated the world’s first known archaeological work".