17 May 1942 "From Washington DC, United States, Ernest King sent Chester Nimitz a message noting that King was now in agreement with the theory that Midway Atoll was likely one of the primary targets in the upcoming Japanese offensive."
However in this scenario, the more important date to me is when did the US request Britain send their carriers to help the USN? Here's the minutes of the
Acadia Conference, maybe it's in here, I'll dig through later. But for now, regardless of the target the US knew from intercepts that the IJN was planning a big offensive, so with the Lexington gone and Yorktown crippled now might be the time for the US to repeat its earlier request for British carriers, especially as Coral Sea was a fight defending UK/AUS territory in which Britain nearly ignored participating in whilst their own three carriers were sailing around the IO.