Whisk water, salt, and sugar together in a large bowl until sugar and salt are completely dissolved.
Cut salmon along one side of the center connective tissue to the skin but not through. Turn the knife parallel to the cutting board and cut salmon meat from skin. Repeat for remaining side and discard skin and connective tissue. Cut each fillet into 1/4-inch slices.
Working in batches of 5, place slices in brine for 3 minutes. Remove cured slices using a slotted spoon to a wire rack and blot gently with paper towels. Arrange salmon in a single layer on a platter, cover with plastic wrap, and refrigerate until chilled, 2 hours to overnight.