In Zweites Buch (Hitler's follow-up to Mein Kampf) he addresses his opinions on the U.S. and his view of the long-term future of Europe. Straight copy-pasta from Wikipedia:
"Hitler declared that for immediate purposes, the Soviet Union was still the most dangerous opponent, but that in the long-term, the most dangerous potential opponent was the U.S."
He viewed America as a mixed bag... "racially degenerate" because of immigration from all corners of the world... yet also having an impressive base of German-Anglo leadership including some of the strongest eugenics projects outside of Germany.
I think at the very least, we can fairly assume that he underestimated our economic/manufacturing potential and what that would mean to the war. He saw it more than most people did, he says so in Zweites Buch, but I don't think anyone grasped the scale of the war machine the U.S. could become, and he probably underestimated the timeline it would take to develop.
The US was already engaging in Europe before the declaration of war through Lend-Lease and similar policies. The US Navy was guarding merchant ship convoys between the US and Britain. German U-Boats, in turn, ended up sinking a couple of destroyers in late 1941. After the sinking of the USS Kearny, Roosevelt gave this speech declaring a planned increase in military capabilities in the Atlantic. The Germans cited the speech in the declaration of war delivered to the US.
In other words, things were ramping up well before the declaration of war. The Germans had every reason to believe that the US would eventually enter the war and the US was already aiding the Allies.
The US declaring war on Japan and the Tripartite Agreement provided a convenient reason to openly declare war.
This question depends on the common misconception that the United States was not already engaged in war in the European theater before the Pearl Harbor.
American ships were actively hunting German U-boats in the North Atlantic at least as early as July of 1941. American aircraft and ships, with American crews and flying the American flag were fighting Germans with casualties and lost ships on both sides for months before the declaration of war. Further than this, the USA was essentially allied with UK giving them all the direct support they were capable of giving. The American leadership was clearly intent on being a part of the war, only delaying actual declaration of war mostly due to PR reasons and because there was no actual reason to do so yet, while their army was still being raised.
Pearl Harbour was a convenient excuse to shut up the isolationists, and a nice flag to rally the people around, nothing more.
While I'm no historian, my understanding was that, yes, of course the US was certainly invested/involved in Britain and USSR's Lend-Lease aid, as well as the sinking of German Uboats, but FDR did not have the congressional backing of an all-out engagement in the European theater (the Pacific was a go); and that in fact it was Germany's/Hitler's declaration of war on US in the wake of pearl harbor which made FDR's argument to the isolationist, pro-facist and anti-communist elements in congress all the easier. War was all but inevitable, but FDR still had to make his case to congress and the American people before getting entrenched in another European war. At least that was my understanding.
Hitler declared war on us in order to honor the Tripartite Pact he signed with Imperial Japan and Italy. He thought that we would be completely crushed in both fronts since Hitler was enjoying dominance over Europe at the time. At the end, he was proven wrong.
As far as for staying out of war, we were involved in lend-lease program with Britain and the Soviet Union because FDR was strongly opposed to Nazi tyrannical expansion around the world. It would be likely that the US would have entered the war sometime in 1942 but that still remains in speculation. The American people at the time was opposed to their intervention in Europe since they felt it was none of their business. They felt they were tricked by the Allies into getting in World War I which they had no interest in so they had to be convinced with something that we have to enter World War II.