No. On January 30th, 1933 President of the Weimar Republic Paul von Hindenburg appointed Hitler as Chancellor and thus the head of the government that was sworn in during a brief ceremony in Hindenburg’s office.
Contrary to a popular misconception, under the Weimar Republic, the Chancellor was a fairly weak figure. He (it was always a ‘he’) served as little more than a chairman of the Council of Ministers.
Cabinet decisions were made by majority vote and due to the difficulty of securing a majority in Reichstag, required cooperation of the President. Who thus was a far more powerful figure than the Chancellor.
And even in this weak government, the Nazis had only three positions out of eleven – Chancellor (Adolf Hitler), Minister of Interior (Wilhelm Frick) and Ministers without portfolio (Hermann Göring).
Consequently, it was not the Nazi Government, but a coalition government where the NSDAP was in the minority. Which gave the latter nowhere near the power they needed to implement political, economic and social reforms, kill the Weimar Republic and replace it with the totalitarian Third Reich.
Nazis got that power (and thus genuinely came to power) exactly a month later – on February 28th (the next day after the Reichstag fire) when Hindenburg signed the Verordnung des Reichspräsidenten zum Schutz von Volk und Staat (Decree of the Reich President for the Protection of People and State) which abolished many of the key civil liberties of German citizens and provided the Chancellor with essentially dictatorial powers.
However, the Nazis acquired the absolute political power in Germany, essentially putting an end to the Weimar Republic and giving birth to the Third Reich, only on March 24th when both Reichstag and Reichsrat (the upper house of the German Parliament) passed the Ermächtigungsgesetz (“Enabling Act”).
The Enabling Act was the constitutional amendment that gave the German Cabinet – in effect, Chancellor Adolf Hitler – the power to enact laws without the involvement of the Reichstag thus placing both legislative and executive power in the hands of one individual – the Führer of Germany.