The short answer for your question would be: yes, it was a term coined/invented by the national socialist German government after 1933.

The term Gottgläubig was introduced in 1936 as an option on census questionnaires and registration offices to answer the question of your religious believe. It described people that left one of the two big churches, but still believed in the Christian god. Before the Nazis introduced the term Gottgläubig, the term Dissident was used in its place. It was an attempt to create a new form of religious identification for national socialists beyond the churches. Gottgläubig also symbolized a close link to the Nazi movement to those that chose it to describe their religious believes with that term.

Dissident defined separatist groups in Protestant and Catholic confessions during the reformation in Poland and the term evolved from there to become a legal term and a concept of self-identification among materialistic and atheistic groups. The Nazis banned the usage of the term in 1936 in favor of gottgläubig because it was also used since the German revolution of 1848 as a form of a political term with the meaning it still has today in the German and English language. The political meaning gave the religious term a negative spin. A dissident was nothing positive in the general reception - so the Nazis came up with a new term to get rid of the negativ connotation. To turn away from the church should be something positive, something people should be able to do unhindered by an old term with more than one meaning.

Sources:

• Cornelia Schmitz-Berning: Vokabular des Nationalsozialismus (2007), pp. 281-288.

• Krause/Balz: Theologische Realenzyklopädie, Bd. 8, p. 558.

• Conze/Frei et. al.: Das Amt und die Vergangenheit. Deutsche Diplomaten im Dritten Reich und in der Bundesrepublik (2010).

• Martin Dehli, Dissidenten: Die Geschichte eines Begriffs weltanschaulicher Pluralisierung, in: Archiv für Begriffsgeschichte Vol. 43 (2001), pp. 173-198 (https://www.jstor.org/stable/24360997).