First off, there is a pedantic mistake in the question itself: Germany did not exist as a unified nation until 1990. East Germany was a communist dictatorship until the very end and did not have a process of democratization. We'll ignore that and examine the West German democratization process.

West Germany's political system, and indeed existence, was shaped by events and tensions following the end of WWII and the immediate freezing of relationships that was the Cold War. The Western powers (US, UK, France) never really liked the Soviets, and since the Allies after WWI had intervened in Russia's civil war, the Soviets didn't have any love for the West either. France was still recovering from Nazi occupation, Britain was spent from the war and was undergoing a process of decolonization in its vast imperial holdings, and the United States did not have the manpower or political will to occupy Europe, given the distance. On the other side, Stalin's Red Army remained menacing mobilized, and although it was heavily battered from the push to Berlin, it was in the field, unfriendly to both the Germans and the West, and Stalin wasn't known for his diplomatic light touch.

Germany proper was split into four occupation zones post-war, French, American, British and Soviet, and after a few attempts to work together on its governance, issues on how to restart the economic engine of Germany failed to reach consensus, with the allies minting the new Deutschemark and the Russians blockading Berlin. The Berlin Airlift would mark the official start of the Cold War, and the Americans, like in every global war in the 20th century, had two big problems. They were called the Pacific and the Atlantic. The frontline between the Communist and the West was drawn across the North German Plain and the Americans could not be expected to man the trenches so far from home. Western Europe, and especially the Germans, had to not stand behind the Yanks or even side by side with the Yanks, but in front of them.

To facilitate this, a series of interlinked economic, diplomatic and political policies were launched between 1944 and 1949 to turn Europe from war-torn wasteland into the new bulwark against the Red Menace. The Europeans needed to want to defend the liberal democratic systems which were America's natural allies. The economic side was the Bretton Woods system and the Marshall Plan, creating the international monetary system and pumping American subsidies into Europe; rapid economic recovery reduced starvation and civil unrest which may cause Communist leanings in the people. On the diplomatic side was NATO, which linked the West by treaty obligations, and politically, the Federal Republic of Germany was established by combining the three allied occupied territories.

In order to facilitate this rapid revitalization of German society, the new Republic needed bureaucrats. From lawyers to chief of staff, Germans who knew how to run a country were needed to ensure continuity. And while the idea of a "clean Wehrmacht" has been repeatedly and thoroughly debunked, it should be noted that the Nazi Party penetrated every aspect of German life, and anybody with any sort of technocratic skill would have had to join the Nazi Party regardless of their personal alignment with its twisted philosophy. This did mean that the crimes of Nazis outside of the highest echelons were swept aside by reformed bureaucrats and that total justice was denied, but this continuation of institutions from not just the Nazi era, but all the way to the founding of Germany itself in 1870, did contribute to the rapid recovery of the nation. Remember, the creation of the new German state was ideological expedience in the face of a very real geopolitical issue with the threat of nuclear war hanging in the balance.

The subsequent democratizations throughout the 20th century were slightly different. Most of the nations which embraced liberal democracy in the post-War 20th century were former colonies in some form or another, and were definitely part of the larger geopolitical struggle of the Cold War. This created two discrepancies between Germany and these later systems: first, the colonial institutions, which were designed first and foremost for resource extraction and the benefit of the Imperial overlord, was far less useful in providing institutional continuity to the nascent democracy, and second, since Europe was seen as the frontline, other nations did not receive the economic, diplomatic and political attention from the West that Europe did. In many cases, a strongman or a junta that had a vested interest in suppressing Communism was an easier and more reliable solution to securing the flanks of the West (A.K.A Containment) than injecting money and political effort to establishing a democratic system where there was never a history of democracy, and where a populist flip towards communism was a possibility.