After two years in Rome, Averbuch continued her studies in Belgium and in 1930 she received a diploma in architecture from the Royal Academy of Arts of Brussels.

After that she opened an independent firm together with architect Shlomo Ginsburg, nicknamed Sha’ag, a graduate of the first class at the Technion and the first architectural faculty in Palestine.

The large immigration wave of middle class German Jews in early 1930s led to a building spurt in the city.

In 1934 Averbuch won a competition for the design of a municipal plaza, Zina Dizengoff Circle, which became the city's central public space and symbol of its modernization.

In 1935 Averbuch married Chaim Alperin, the first commander of the Tel Aviv Police and one of the founders of the Israeli Red Cross (Magen David Adom).

Her work includes pioneers' houses (residences for single women) in Jerusalem (1942) and in Netanya (1950), and agricultural youth villages for children and adolescent Holocaust refugees (Kfar Batya, 1945; Hadassim, 1947).