The League of Nations was not the first international organization of its type. For that you need only look to the
Concert of Europe which was established in the aftermath of the Napoleonic wars. It too suffered a similar fate to the League of Nations: becoming increasingly irrelevant and finally becoming officially defunct with the outbreak of WWI.
I think the best way to preclude the formation of the UN would be to make the schism between the Soviets and Western Allies more bitter following WWII. So much so that the Eastern Block countries refuse to try and even join such an organization (most likely seeing it as little more than a "capitalist sham"), which would pretty much just turn the UN into an international alliance like NATO and others which had preceded it before.