 Johan Martin Quist was born in Copenhagen, the son of Nicolaj Mathiessen Quist, a shoemaker, and Anna Marie Elisabeth Engelbrecht.After being trained as a mason, he studied at the Royal Danish Academy of Fine Arts under the influential Caspar Frederik Harsdorff, winning the large silver medal in 1775 and the small gold medal in 1781.Quist was one of the Copenhagen builders who so quickly and effectively helped to reconstruct the areas of the old town which had been destroyed by the Copenhagen Fire of 1795.