This is an appallingly simplistic view of the war. I don't think a lot of people realize how close the Allies were to collapsing before the ill-fated (for the Axis) attack on America's assets in the Pacific. There is too much separating of "Nazis" and "Germans". They were all in it together (whether all of them wanted to be or not) and all of the people that history wants to drop into neat little baskets had their strengths and their weaknesses.
It is just such a failure to understand history that doomed Germany in the 1940's.
The Axis, insomuch as it was a functional alliance, was a rather loose one.
Nothing about it really compelled Hitler to declare war on the U.S. once the Japanese began their war in East Asia. Hitler did it for his own opportunistic reasons.
The main ones included...
(1.) The U.S. was essentially fighting an undeclared naval war against the Germans with the British in the North Atlantic. The Kriegsmarine was absolutely begging Hitler to turn them loose against the U.S. Navy and shipping assets, claiming they could possibly starve the British out of the war (which the Germans were
much closer to doing in the 1910s) or, at least, affect the flow of Lend-Lease supplies to the Soviets to affect the strategic and supply situation on the Eastern Front or even starve the Soviets out, so much as Stalin cared.
They were not entirely wrong, by the way. Allied shipping loses were incredible for the first year or two of the Battle of the Atlantic, and American/British strategic options in Europe were very limited by their lack of shipping from North America to back it up. It took three years for there to be an Overlord because it took three years to win the Battle of the Atlantic.
(2.) Hitler had some appreciation for the industrial might of the U.S. and the depth of its manpower, but he considered it a "mongrel nation" controlled by Jews that would take far too long to spool into a wartime footing to really matter before he knocked the Soviets out of the war. This was by far his largest miscalculation in this situation. Turning the U-Boats loose made some sense as a strategic gamble. This was just pure Nazi ideology and German nationalism blinding him where a more somber observer would have realized the problem.
(3.) And least importantly, he essentially promised the Japanese he would, and he thought these little "yellow men" could distract the Americans somewhat.
Yes, the low point for the Allies was right before the American entry into the war, but how exactly do the Germans win at that point? They still would have been unable to take Moscow by the end of 1941, and I doubt 1942 goes much better for them. It might still end in Stalingrad. They still lose the Battle of El Alamein and fall back across Libya. The loss of the distraction from the American landings in North Africa is made up for unfettered American shipping to the British Isles and even up to the White Sea ports to supply the Soviets. That trade is a wash.
How exactly do the Germans win?
I can give you a half-dozen times they almost won the first time, but zero the second.