Schwab was born in 1899 in Berlin as the second son of famed journalist  and his wife, the writer Marie Köglmayr. Both his parents originated from Bavaria; Josef Schwab was a Franconian Jew and his wife a Catholic from Upper Bavaria. Georg-Maria finished his secondary education at the Friedrich Wilhelm Gymnasium in Berlin, and upon turning 18 was conscripted for WWI and served for a year with the Bavarian Army in Flanders.
Following WWI, Schwab studied Chemistry and Physics in the University of Berlin. He continued his postgraduate studies there under the supervision of Ernst Hermann Riesenfeld and in 1923 received his doctorate with his thesis "Über Ozon" (On Ozone), which was awarded the rare distinction eximium opus. For the following two years, until 1925, Schwab worked as a research assistant to Max Bodenstein, the successor of Walther Nernst in the Institute of Physical Chemistry that Nernst founded in Berlin. Under Bodenstein, Schwab was initiated and trained in the field of chemical kinetics, in which he contributed much for the rest of his career.
In 1925, he accepted a position in the University of Würzburg, initially as the assistant of Otto Dimroth. He was eventually habilitated in 1927 as a Privatdozent in Würzburg with his habilitation thesis on the thermal decomposition of methane and ammonia. In 1928, after the invitation of Heinrich Otto Wieland, Schwab began working in the inorganic laboratory at the University of Munich and was promoted to extraordinary professor in 1933.
It was during this period that he met his future wife Elly Agallidis (), a Greek physicist who was doing her PhD in the University of Munich.
Schwab remained at his position in Munich until 1938, when he was expelled and barred from teaching by Nazi authorities on account of "racial grounds" i.e. his half-Jewish origin. Raised a Catholic, he had been previously unaware of his father's origin until questioned about it under the provisions of the 1933 anti-Semitic Civil Service Law.