The Ju-390 was a real plane with 6 engines and the range to fly to New York and back. There is no reason to believe that one of those that were produced didn’t fly there as reported. One also flew a polar flight to Japan in 1944.
I think if Germany would have won the war quickly against the USSR like it had planned and if Britain then were forced into a peace with Germany like Hitler had wanted after Dunkirk things would have continued on Earth much the same way the cold war did with the Nazis taking the place of the Soviets, only more powerful. It may have even been a friendlier cold war. The heavy water plant would not have been attacked which means that Germany would have acquired the bomb earlier and since they already had bombers that could reach America it would have eventually meant a draw, that is if America would have started and continued with the Manhattan project.
America didn’t go to war to liberate Europe in the real WW2 so it is doubtful that they would have in an alternate outcome against a more powerful Germany. Besides, without the USSR and the other western allies to help, America alone would have been no match for Germany.
Hitler never had a desire to conquer America or the whole world anyway. In that scenario the Germans would have been the first on the moon and America, less the technology that it looted from Germany after the war, would have been far behind in rocket science and other technology and never would have caught up. The Germans would have eventually put nuclear warheads on their rockets to reach anywhere in the world and the Americans, if they eventually acquired the bomb, would have had to rely on dropping them from bombers. The Jews would have been wiped out of course which would have meant peace in the Middle East. Perhaps no one would have even ever heard of Iraq today. Or terrorists.
But in the end all empires fall and so would have the Third Reich.