In a way it seems a little counter-intuitive. The whole endgame in Europe was the destruction of Nazi power, so why would they set up a form of government that would hypothetically let another extremist party gain influence in the future? How could they be sure that Germans would vote for moderate, anti-military parties?
Democracy in Germany led to the rise of the Nazis?
That is really an ultra simplification of the facts. What led to the rise of the Nazis is a deeply ingrained denial of the WW1 defeat.
Even after the defeat they refused to believe that they had been beaten, it is basically because of the fact that German defeat was mainly an economic defeat. On the field the German soldiers were still fighting and even though they had been slowly giving ground to the French and British for about four years almost without interruption some still believed the situation could be turned.
When the ceasefire got signed, the German soldiers came back home not looking like a beaten army but with all their weapons and equipment, which along with the actions of some anti war politicians during the war began the legend that the German army had not lost the war but had been stabbed in the back by politicians / jews / jewish politicians / speculators / whoever is fashionable as scapegoat at the moment (as the main German pacifist politician during the war was Jewish the Jews were of course among the main suspects in the mind of people).
Adolf Hitler, a random WW1 vet then joined the NSDAP (an obscure group of far right conspiracy theorists) as a mole of the German military intelligence but got seduced by the discourses of Dietrich Eckart, the leader of the NSDAP, who was an advocate of the "Jews caused the WW1 defeat by betraying the glorious German army which was valiantly fighting" theory.
Hitler then got remarked for his amazing oratory skills and ended up taking the head of the NSDAP. Years later Hitler is chancellor and the rest is history.
Directly linking the democratic form of government to the rise of the Nazis is a bit too big of stretch sincerely.
By dividing Germany in the way that they did (the four zones, French, British, American, and Soviet), the Allies were making a firm commitment that Germany would not be allowed falter as it did in the 1930s. And the military forces involved in Germany (which quickly turned into anti-Soviet forces as the Cold War developed) were there to protect German democracy.