Could the Germans have won?

We now think of allied victory in WWII, which set the pattern for the rest of the 20th century, as inevitable.  America, Britain, and Soviet Russia had a vastly greater population, vastly great industrial capacity,  and all the natural resources needed to fight a war.  But,  you need to look at the world as it was in 1940, Hitler's high tide.  His armies had crushed Poland and then France, occupied Denmark, Holland, Norway, Belgium and Luxemburg, and driven the British into the sea at Dunkirk.  Hitler owned most of Western Europe.  Britain alone stood in opposition. 
   Starting from this high point, what could the Germans have done to win the war, and dominate the world, probably until today?  To be real about, or even semi real, we have to have Hitler running Germany.  Without Hitler, we would not have had WWII.  In 1940 everyone in Europe remembered the horror that was WWI, only twenty years in the past.  Nobody, except a madman, which Hitler was, could think that any diplomatic gain, territorial expansion, anything at all, was worth doing WWI over again.  If Hitler is removed from the scene, say by assassination in the 1930's, the world would have been spared WWII.  Under any other leader, the Germans would have thrown their weight around, and obtained concessions, but they would have not sent their army into Poland in 1939. 
    First of all, Hitler could have gone for the bomb.  It was Otto Hahn, a German physicist working in Germany, who discovered nuclear fission in 1938.  If the industrial resources the Germans poured into the fairly useless V2 rocket program been applied to creating nuclear weapons, Germany might well have been able to nuke London or Moscow by 1944. 
    Second, Hitler could have polished off the British in 1940.  This would have destroyed one of the three great allied powers.  It would have allowed Hitler to throw more force against the Russians in 1941 without the British sniping at him from the West.  It would have deprived the allies of the airbase from which the RAF and USAAF  bombed Germany flat by 1945.  It would have captured the launch pad for Operation Overlord, which sealed the fate of Germany.  Overlord's vast armada of shipping was largely short range shallow draft landing craft, seaworthy enough to cross the Channel in good weather, but incapable of crossing the Atlantic.
   The British Army had abandoned all their tanks, artillery, motor vehicles and heavy equipment at Dunkirk.  Only a few troops still had their rifles when evacuated to England.  Had the Germans put three or four divisions ashore in England that summer, the place would have been theirs.  The trick was to get those divisions across the channel in the face of the Royal Navy.   Barges and landing craft full of troops are dead meat when the British steam up along side with a battleship.   The German counter to the Royal Navy was the Luftwaffe.   Air attack with bombs and torpedoes will sink anything that floats.  The Luftwaffe needed to achieve air superiority, namely beat down the RAF to the point where the slow and vulnerable Stuka's could operate over the channel without being bounced by RAF Spitfires.  The Luftwaffe nearly achieved air superiority during the 1940 air battles, doing it the hard way,  flying into British airspace and dog fighting with RAF Spitfires and Hurricanes.  If they had concentrated upon knocking out the coastal radar stations, the sector stations, the air fields, and the aircraft factories they might have done it.  All the British accounts of the Battle of Britain stress how close the Germans came to winning it. 
   Thirdly, Hitler could have given Rommel and the Afrika Korps more support.  Rommel only had a couple of German divisions, going up against the British with eight to twelve divisions.  A couple more divisions for Rommel taken from the 140 sent into Russia would have made all the difference in the middle east but wouldn't have made much difference on the eastern front. If the paratroops sent to take Crete had been used to take Malta instead, Rommel's supply lines across the Mediterranean would have been secure.  Had Rommel taken Egypt, the Suez Canal, and the Iraq oilfields it would have solved Hitler's fuel problems, and dealt a crushing blow to the British. 
   Fourth, Hitler could have refrained from declaring war on the United States after Pearl Harbor.  He had made no binding treaties with the Japanese, he didn't owe them anything.  As it was, he made Roosevelt's job in pursuing a "Germany First" strategy far easier.  And he drove the last nails into the American isolationist's coffin.  Without Hitler's gratuitous declaration of war, the isolationists might have kept America out of the European war for months and months.  For Hitler, locked in a death struggle with the British and the Soviets at the time, a delay of months in American belligerency is not to be sneezed at. 
   There are others, but the first four above are enough for this post.  And a world where the Third Reich won would have been very bad indeed.