re: When did the German soldiers of WWII realize they were the 'bad guys'?

Some things that people should keep in mind when they wonder why Hitler declared war on the USA -- here's a list of what the USA had done to help the Allies prior to Hitler declaring war on the USA:

1) Shortly after the Fall of France, the USA provided free 100 Octane aviation fuel to the Royal Air Force. The RAF was greatly aided during the Battle of Britain with this fuel. The Luftwaffe had no access to that powerful fuel. The RAF's fighter force was fully outfitted with 100 Octane fuel for the Battle of Britain and this would have been impossible without the USA's gift.

2) The USA provided free materiel support to both Britain, and, after 22 June 1941, Soviet Russia. The USA's "Lend Lease" shipments to Soviet Russia began ASAP after Hitler invaded Soviet Russia. This aid was extensive even in 1941.

3) The USA provided as much materiel aid for Britain as they could AND the US Navy and US air power were both committed to protecting Allied shipping over the Atlantic Ocean. This US protection included engaging in combat with the Germans.

So, by the time that Hitler declared war on the USA, the USA was already fully engaged in helping the Allies. The US Army was already mobilizing and preparing to enter the war against Hitler beginning in 1940, and that mobilization continued into 1941.

Yes, Hitler miscalculated very often. Hitler didn't expect Britain and France to Declare War after Poland was invaded in 1939. Hitler expected Britain to make peace after France fell. Hitler had no idea that the Soviet Union could generate such military might and force projection. Hitler didn't think that the USA's industry and armed forces would be powerful enough to help defeat Germany.

So it is true to say that Hitler declaring war on the USA was a miscalculation BUT it is important to understand the question in its full context, and that context is that the USA was already waging an undeclared war on Germany for many months by the time Hitler declared war on the USA in December 1941.

The USA was NOT going to stop waging that undeclared war against Germany whether Hitler declared war or not.

And once the US Army was ready to fight on foreign shores against the Germans, the USA would have declared war on Germany, probably shortly before the North African Operation Torch landings in November, 1942.

. . . all in my own humble opinion, of course.