In actual fact the Normandy invasion was not a significant contributor to Germany's defeat. A small US/British/Canadian/French force of about 150,000 soldiers of which about 73,000 were American faced a few German divisions at half strength and short of fuel and ammo. The real war was on the Eastern front where millions of soldiers had been fighting for several years.
The Red Army won World War II. The cost to the Soviets was between 9 million and 11 million military deaths. Adding in the Russian civilian deaths, the Soviet Union won the war at the cost of between 22 million and 27 million Soviet lives.
In contrast the US had 405,000 soldiers killed during WW II of which 111,600 died fighting the Japanese in the Pacific.