He was admitted to the Royal Danish Academy of Fine Arts in 1900 but dissatisfied with the teachings, left just two years later and was instead articled to Peder Vilhelm Jensen-Klint.

At Jensen-klint's and Wenck's office, he was part of a group of young like-minded architects which also included Ivar Bentsen, Carl Petersen, Hans Koch and Thorkild Henningsen and with whom he founded Den Frie Arkitektforening in 1909.

[3] Over the next years, he designed a number of large villas and country houses, mostly in Copenhagen's affluent northern suburbs or in North Zealand.

They were followed by a number of other housing estates, including Møllegården at Amager Boulevard, Grønnegaarden at Borups Allé, Classens Have on Classensgade and Linoleumshuset in Åboulevard.

From around 1930, Baumann's work was increasingly influenced by the Modernist trends of the time, This was for instance the case with the office building Ved Vesterport, designed in collaboration with Ole Falkentorp in 1930–31.