Brust was born in Frankfurt, Germany in 1897, and as early as 1913 was apprenticed as a lithographic printer. He studied at the Kunstgewerbeschule, Offenbach with teachers Rudolf Koch and Richard Throll, among others.
From 1919 he was a freelance artist--until 1931 when he settled in Berlin. In 1933 his portrait of Hitler was exhibited in the Berlin Secession exhibition, Hamburg, but later in 1933 he was denounced as a ‘Kulturbolschewist’ and was no longer able to exhibit his work until after the war. A 1937 article in the journal Gebrauchsgraphik features his work for posters and covers for the magazine Die Sirene (1935). Much of his work was destroyed in bombing raids. From 1949 he became the picture editor at the publisher Martens, Munich.