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If Hitler hadn’t declared war on the US, he stood a chance of beating the Soviet Union, or at least securing a negotiated truce. Once he declared war, all bets were off.

True, but irrelevant - Hitler could not avoid declaring war on the US. He would have lost face if - as he expected, based on publicly leaked Rainbow plans - the US declared war on him. First.
You might as well argue that Germany could have easily defeated the USSR by the simple strategem of liberating Russians from Communism. Perfectly true - and, if you read Mein Kampf, perfectly beside the point of who/what Hitler was. The whole point was to turn Eastern Europe into part of Germany. On the basis of race.

Freedom's Forge:
How American Business Produced Victory in World War II
Arthur Herman
explains why America had minimal military inventory upon entering WWII, but very quickly dominated the military logistics equation. FDR initiated industrial mobilization upon the Fall of France at the end of May, 1940. He asked his main man in that effort how long it would take to make the machine tools and factories required, and was told eighteen months. Amazing the coincidence between “eighteen months after May 1940” and “December 7, 1941” . . .

[True, but irrelevant - Hitler could not avoid declaring war on the US. He would have lost face if - as he expected, based on publicly leaked Rainbow plans - the US declared war on him. First.]

The US would not have declared war on Germany if Hitler had not done so first. Popular opinion against US participation was simply too strong, influenced, undoubtedly, by the large German- and Italian-American populations (and other ethnics from the Axis countries) who were not particularly thrilled about having to fight their co-ethnics from the old country. Hitler’s declaration of war swung that around.