[Homer_J_Simpson]

'Weapons are not to be used. Even if American vessels conduct themselves in a definitely unneutral manner. . . . Weapons are to be used only if US ships fire the first shot.' ”

So if the Germans really were winning the battle of the Atlantic they were doing so with a major self-imposed constraint. Didn't Hitler severely limit the number of U-Boats operating in American waters?

[BroJoeK]

Homer: "So if the Germans really were winning the battle of the Atlantic they were doing so with a major self-imposed constraint.
Didn't Hitler severely limit the number of U-Boats operating in American waters?"

My understanding is that Hitler didn't fully appreciate the importance of his U-boats, or how close they came to winning the war for him.

But it wasn't just the lack of numbers, it's also the fact that German U-boats of WWII were not so advanced beyond those of WWI, until far too late in the war.
It's one of those great "what ifs", however, none of that was readily apparent in May of 1941.