Allowing Hitler to rearm, without consequence was an even bigger mistake.
If Hitler hadn't made the classical mistake of waging a war on two fronts by attacking Russia (presumably to get control of their natural resources), then he may have been ruling the world within a decade.
Thankfully, he was both mad and egotistical, which is what saved the world.

@Magister He might have ruled part or most of Europe for awhile, but it would have been difficult. He had no access to enough oil to run his giant oil machine. He could never come up with a large enough Army to hold on to all of that. He could never have conquered the U.S. Geography is our friend. You can nuke us, but you can't conquer us and control that many millions of people. Kicking a big country's ass and ruling them are two different things.

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@Sticks48 By picking off countries one by one, he would have (as I have already alluded to} been able to use their natural resources to fuel his war machine.

If he had conquered the UK, valuable intelligence gleaned from the Colossus computer that had cracked the Enigma machine, could be directed towards the USA.

The enemy engagements of the British and Norwegians would not have happened and Germany would have been producing enough heavy water to ensure that their nuclear programme would have been a success.

His scientists would have perfected the first intercontinental missile, base upon his successful V2, then a massive bombing campaign would have struck America, again, he would have had access to the British Empire's natural resources which was from an Empire that spanned three-quarters of the globe.

He would also have enslaved the people of conquered countries into building launch sites and building his jet planes and other armaments and he would have found plenty of volunteers who would have joined his Wehrmacht.

There were plenty of volunteers who joined the SS to form SS legions built from their own country's citizens.

Belgium had one, for example, as did France, half of which was Vichy, which actively collaborated with the Nazis to rule France.

America would have stood alone and would have been no match from what would have become a Nazi superpower that ruled most of the globe.

Just as, Great Britain ruled a massive empire, as did the Romans before, they did so with a very few colonial rulers helped by the inhabitants of the countries that they conquered.

Again, he would have been able to use the American Nazi Party to assist in acts of sabotage, intelligence gathering and recruitment to help in his conquering America.

No doubt Mexico would have joined in the fight, as they may have done in the first world war had Great Britain not given America a decrypted signal from Ribbentrop to the Mexican government warning them of this.

With no allies to help, America would have fallen and Hitler would have continued with his programme of wiping out Jews and anyone that he deemed to be a threat.

Don't ignore how close a run thing this war was, or be blinded by patriotism into thinking that America was invincible ; it wasn't and it required the might of all of the allied forces, along with good luck, to defeat the Nazis.

The brilliance of Nazi scientists was well known, which is why America launched Operation Paperclip, during the last days of the war, to snatch them up, so that their knowledge could be used by America.

This included many Nazi war criminals, such as Werner von Braun who developed the American space programme, who ought to have been hanged for war crimes at Nuremburg.

This was a particular travesty of justice for the Londoners and slave labour who died from his rocket programme, whilst he was given American citizenship and a new life.

So, Hitler could have easily defeated every single allied country, if only he had allowed his generals to run the war unhindered by his poor judgment.

@Magister As ridiculous a scenario as a Star Wars movie, but you have a great imagination. You act like the US and Russia would have just watch all of this happen. You obviously have a great imagination, but that whole thing is laughable.

@Sticks48 I'm afraid that you are allowing your indoctrination, and lack of knowledge, has blinded you to the realities of that war. All of this has been historically documented and just a little research will prove this not to be just imagination but based on fact.
Fact. Hitler had signed a non-aggression treaty with Russia, which was honoured until Hitler invaded Russia.

Fact. The communist revolution meant Russia was not prepared for war, and it couldn't even arm all of its soldiers. Their success was due to the blitzkreig attack pushed too far ahead of its supply train, that German troops were unable to capitalise on its gains, and the omcoming winter greatly aided them, along with its willingness to sacrifice huge numbers of men in suicide attacks.

Fact. Vichy France helped Germany in administrating the country and aided in rounding up Jews.
Fact. Germany used men from conquered countries to work as slave labour in its armaments industry and infrastructure building, including the V2 rocket sites at places suvh as Peenemunde.

Fact. Winston Churchill, in a desperate bid to get America to leave its neutral stance told the president that if Great Britain fell, Hitler would concentrate on defeating America, with success, and he meant it.
Fact. The SS established units based upon volunteers from occupied countries, such as Belgium, whose Walloon SS unit were highly decorated and were led by a Belgian political leader.

Fact. Operation Paperclip did save many Nazi scientists from the hangman's noose, and it was (in part) from a fear that they would fall into Stalin's hands and give them the edge in military and nuclear technology.

It would take me too long to put in all the links to factual documents that establish my outline as not being mere conjecture, but I suspect that you wouldn't read it and you would choose to ignore it in favour of your position which is based upon your idea that America is invincible. It wasn't then, and it isn't now.