How did the cold war grow out of World War 2?

By the time Germany surrendered to the Allies in early May of 1945, both the Soviets and Americans had significant control over Germany, Soviets taking East of Germany, and the allies of West Germany (That's how Germany was divided into two).

When the war was over in August after Japan surrendered, it was then a matter of who at that time was the worlds Superpower nation, both military and economically. It could never be certain at the time since Russia and America took over Germany at almost the same time, none of them took full control over Germany.

And so that's why suring the 46 years of the War, both the USA and USSR were building up their Military power, economic stability, political influences and most importantly the Space and Arms race. All because even though Nazi Germany surrendered to America, there was no nation that conquered all of the Third Reich