The downward view window was seen on most if not all of the early U.S. monoplanes for different reasons. In the case of the TBD, the Norden bombsight was located there. The bombardier crawled under the pilot and lay on his belly to use it. in most, like the SBD and F4F, it was probably there to restore some of the downward visibility to the monoplane pilot, who was positioned more over the wing than the biplane pilot. However, in the case of the F4U, like its competitors the XFL-1 and the XF5F, it was also there so the pilot could aim little bombs housed in little bomb bays in the wings and drop them on bombers below. In this picture from the Grumman archives, its the dark area underneath the cockpit. The hole in the cockpit floor was located between the base of the stick and the instrument pane. The antiaircraft bomb capability was deleted from the XF4U but the window remained in early production.
Oh, and in case you didn't notice, one of the main gear door linkages broke on this test flight so the door didn't close.