I was curious to try and find out how fatigued the soldiers involved in D-Day may have been before they landed. I've tried looking on the internet and cant seem to find a result for how long the soldiers had to stand in the Landing Crafts before and en-route to the landing zones.
The convoys carrying troops departed from ports in southern England on the afternoon of June 5, 1944 and proceeded slowly across the channel with heavy air cover. They dropped anchor in their designated transport areas 23,000 yards offshore at roughly 0200 on June 6, at the same time that airborne forces were being landed. Boat teams were assembled, and loading and lowering of landing craft began at 0430, with H-Hour at 0630; so, roughly 2 hours. Elements of the 4th and 24th Cavalry Reconnaissance Squadrons proceeded in their landing craft two hours before H-Hour to clear out a small German observation post on the St. Marcouf Islands off Utah Beach.
Sources:
Omaha Beachhead (6 June-13 June 1944), by the Historical Division, War Department
U.S. Army in World War II, European Theater of Operations: Cross-Channel Attack, by Gordon A. Harrison