From the US and British side there were... let's say trepidations in regards to the first West German election at the possibility of the leftists (SPD) winning, with a similar trend in Italy and France. I believe there were some ideas floated to prop up the rightist parties to deny the SPD any victory, but they eventually supported the CDU.
In addition to that, there was the rumor (which was probably false or barely meaningful) of the Soviets funding the Neo-Nazi and Fascist parties to destabilize the West German government, obviously they would not want said parties to win but to be a thorn in the West Germany's side if the rumor was true.
A Nazi cabal seems like an interesting idea, and a possible one to attempt to push one direction or another with enough support from ideologically inclined industrialists.
Combine these three in a series of unlikely but somewhat possible events where the Fascists once again roll a few sixes and you might end up with a rightist government instead of the possible leftist one. With varying levels of influence from the left and center parties. However, I don't believe a Nazi or a bona-fide Fascist party would be able to win and keep their spoils, those Fascists in power would be more similar to either Franco or Salazar, inclined towards Fascist Corporatism or Neo-Corporatism, which remained somewhat popular in the post war world.
I don't think it is a stretch to imagine them tolerating a Salazar-esque West Germany. Refusing to accept the election results, or outright oust the Corporatists from power would be damaging to the image of the US and her allies, something that the horrified (at the election results) Soviets would gleefully use to turn other countries against the so called democratic bastion.
And the Soviets are the ones who will probably push towards escalation following said election. A Berlin Crisis happening sooner maybe? I admit that after this point I am unsure how the war would start at the hands of Germany, either West or East. I am inclined to say through funding of anti Soviet agitation and outright partisan assassination across the border by the West German government, or support to all resistance fighters (as they were still active up to the 60s throughout Eastern Europe) + Stalin's ideological narrative of an inevitable Capitalist Communist confrontation.
(For the CDU to.. not win the election could perhaps be attributed to worse leadership and campaigning? The Neo-Corporatist members joining the other right parties while the catholic monarchists joining the Bavarian party? People with a better understanding of German post war politics could probably answer this. - I know that support for the monarchy was low even during Weimar, but at the very least, in Bavaria there was a good amount of support so it is an avenue to spread the vote -)
It is perhaps a bit more grounded in reality from the other proposals but it would require some sixes one after the other, not impossible but unlike. Though that's another facet of AH, leaning to the more chaotic and unpredictable side of history but not outright going into the wacky corner.
