Germany already declared war on the USA in 1941. If they had assimilated the power of the USSR into their own (and frankly, Stalin’s ideology was more national socialist than international socialist), it would have been a hot war.
I believe in Mine Kampf Hitler even predicted the cold war being divided into three “zones of influence” with the USA controlling North and South America, Japan controlling East Asia and Germany controlling Europe and Russia west of the Urals). We’ll never know but my contention the cold war would have been about the same just substitute Germany and the Reich for the USSR and the East Block. One side note The Reich would have made it to the moon first, those bastards.