By "first major" I mostly mean "early notable". I searched for information on the topic online but somehow failed to find anything not related to modern dredging efforts and ships. I am writing a fantasy story involving a maritime nation using different types of ports and harbours, and would like to understand how to approach this particular aspect in a historical context.
Thank you for this very interesting question, though I cannot directly answer your question about 'When & Where'.
Many medieval famous ports like Dorestad and Bruges now in Low Countries became almost out of use by the end of the Middle Ages due to the sediment deposition by rivers. While I cannot find a reference to any measure taken by human to keep the sediment coming, some Europeans certainly tried to prevent further artificial damage to the waterways, that is to say, the lifeline to their port towns, at least in the Later Middle Ages.
Latest since the end of the 13th century, we can find prohibitions against the illegal dumping of the ballast from ships into either waterways or the port itself under penalty of 3 marks silver in many cities around the Baltic Sea like Hamburg, Wismar, and Copenhagen. The shipper and sailors were required to deposit such ballast only to a certain assigned places, and town dwellers even sometimes seemed to recycle the deposited ballast for the large-construction activity in their city (Cf. Ansorge et al. 2002 for Wismer). On the other hand, it was the authority's responsibility to provide ships with the ballast, and special officials (names varied in different cities, though) had been appointed to take care of depositing and preparing the ballast for coming and going ships since the late 15th century, and it was one of the duty of citizens living by the port to report any illegal act of damaging the port as well as waterways to these officials. In some cities, violators of these regulations were liable not only to fines, but also forced under the imprisonment or the expulsion from the town. The official earned not only their salary from the city council, but also the third of such fines in Hamburg.
In principle, every citizen were also expected to corporate with the town authority's instruction to clean waterways as well as the harbor. In not self-governing Copenhagen where the king of Denmark was also the authority of the town, foreign visitors had also to follow the instruction of the king to keep the harbor clean. Special tax was sometimes imposed upon the citizens to enforce this kind of cleaning activity, though I cannot find what kind of tools were actually used for the cleaning. To check the primary sources texts perhaps will shed some light on this activity.
In addition to these more 'regular' maintenance activities, Hamburg city council in the middle of the 16th century invested quite an amount of money to improve/ keep waterways clean and navigiable for the large ships by some pavements of logs, sand asnd stones. They also hired two special civil engineers of the Dutch origin, namely Antonius Bardun and his son from Seeland, to fulfill this job in ca. 1540. So, I assume that this large-scale building activity includes some dregding operations as well, and that the Netherlands could be regarded as a pioneer of this field of activity in the 16th century, but I unfortunately knew little about harbors and the building activity there, sorry.
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[Edited]: fixes spelling.