Social Democracy in Germany was already very popular nearly since the foundation of Germany in 1871. The Social Party of Workers (German: SAP = Sozialstische Arbeiter Partei).
The SAP soon became very important for the German working class, which was rapidly growing, because Germany was one of the fastest industrializing countries at the time. Bismarck tried to reduce their influence by establishing some sort of pension and healthcare insurance. However this did not work out as expected. The SAP was also banned between 1878 and 1890. Natural persons could still be elected to parlament, which was the loophole to still candidate for German parlament as some sort of underground party. Later on the SAP was renamed to SPD (Sozaildemokratische Partei Deutschlands = Social Democratic Party of Germany) and still exists today under that name.
The SPD established it also as the main anti war party before world war 1. This was also one of the reasons the party became very popular at the end of World War 1 and during the creation of the Weimar Republic. At the end of the World War 1 a part of the SPD wanted a communist revolution comparable to the one in Russia with the main goal of overthrowing the political and social order. This group was first knwon as the USPD. The SPD itself agreed on reforming the political and social system inside the system without a revolution like in Russia. As a more moderate working party the SPD established itself in the Weimer system and became the first party to rule the new German country. The party remained relevant until all parties got banned after Hitler took over power in 1933. The SPD was still anti war and storngly opposed Hitler. The party was the only party along side the KPD (communist party) to vote against the law, which abolished the power of the parlament (Reichsermächtigungsgesetz).
So overall social democracy was established for a long time in Germany already. In 1949 the SPD once again ran for parlament. Once again the party was mainly for an anti war policy not taking sides in the emerging cold war. The party wanted to stay neutral in order to never again be part of a war. They further wanted to keep on talking to the Soviets in order to achieve a reunion with the eastern parts of Germany under Soviet control.
In Germany the rearmament and the reunification of Germany were the main thematics of the first two elections in the new founded Bundesrepublik. Still many cities were bombed. In the winter of 1946 there were many people freezing to death in Germany and even up to the 1950s some families had to share homes. Thus probably the most important factor of the Marshall plan, that had consequences for the 1949 election, was that Germany was able to import enough cotton for its population. The effects of the plan for the economy were more likely to have impacts on all of the following elections, when Germany economy started to recover.
Obviously there are no hard numbers showing if people had voted differently without the Marshall plan, but it is important to note, that after the 1949 election the parlament in Germany voted their chancellor (in Germany not directly elected). Konrad Adenauer received 202 of the 402 possible votes. So if he had received one vote less he would not have received m ore than 50% of the votes, which would have not made him chancellor.
So to conclude i hope this gives a basic understanding that social democracies has been part of German politics for a long time and that social democracy had more topics to discuss then an economic side. And that the Marshall plan did not rebuild Germany in 1949 ony year after the plan was executed.