Not a historian, but I grew up in Germany.

Basically most of the officers corps seems to have been made up of former Wehrmacht officers. Not surprising really, it takes a few years to get someone to that point.

There also was a group of former Wehrmacht soldiers that had been trying to convince the German Government, and by extension the Americans, that (West) Germany should be allowed to re-arm. The "heating up" of the Cold War made the whole thing rather interesting to the Americans. From memory they were of the opinion that Germany should help in defending the "Free World" and thus it quickly became part of the defence strategy in Europe.

Not sure how the rest of the world saw it, though I suspect the fear of the Soviets was bigger than that of a German Army in a country that was essentially occupied by the Western powers.