Final answer:
The first Navy Mine Disposal School was likely established around or shortly after 1942, during World War II, when naval mines were prominently used and required specialized handling.
Step-by-step explanation:
The first Navy Mine Disposal School was established during a time when naval mines played a significant role in warfare. Historical accounts point to the period surrounding World War II as notably profound for developments in mine warfare. In 1942, the U.S. Navy achieved a significant victory at Midway and began implementing strategies such as mine laying, which required specialized knowledge and skills in handling such explosive devices. The exact establishment date of the first Navy Mine Disposal School isn't provided in the information given, but it can be inferred to have been necessitated during or shortly after this time due to the strategic significance of mines in naval warfare.