Recounting some of Tùng's early life helps situate events later in his career. Tùng was born on 10 May 1912 in Thanh Hóa in the northern part of central Vietnam. When Tùng's father died shortly after Tùng's birth, he moved with his family to Huế. Even though Tùng's mother encouraged him to become a mandarin, Tùng turned to a French education and he left Huế in 1931 to study at the Lycee du Protectoral in Hanoi. After earning his baccalaureat degree at the Lycee, Tùng enrolled in the Faculty of Medicine at the Indochina University in 1934. One year later Tùng was placed as an extern at the hôpital du protectoral (Yersin hospital). While there Tùng became interested in the liver and surgical approaches to its pathologies. As a student, Tùng served as the laboratory assistant for the French surgeon Pierre Huard. While conducting an autopsy on a body whose liver was infected with ascaris, Tùng envisioned a new method for understanding the liver's anatomy. Tracing the path of the ascaris with a curette led Tùng to believe that dissection would better uncover the liver's structure than radiologic exploration or corrosion, the two techniques then in use.

Normally, after completing two years of study, students took an exam to qualify for the post of intern. Being one of the first Vietnamese to apply for an internship, Tùng had to convince the French authorities to allow him to take the exam. In 1938, Tùng became the first Vietnamese intern, a position that allowed him to undertake his investigations on the vascularisation of the liver at the Hanoi Institute of Anatomy as well as to maintain his place at the hospital. In 1939, Tùng defended his medical thesis, La vascularisation veineuse du foie et ses applications aux resections et lobectomies hepatiques, which drew from his experience of dissecting more than 200 livers (Tùng, 1939). The Paris Faculty of Medicine awarded his thesis a Silver Medal. In that same year, Tùng performed the resection of a tumour in the left lobe of the liver together with one of his professors. For this technique, the blood vessels were progressively exposed and ligatured at the point where they entered the hepatic parenchyma. Yet, when the report was sent to the Academy of Surgery in Paris, it was strongly criticised. Moreover, a patient suffering from a massive hepatoma died during the operation. Because of these developments, Tùng had to stop his work on this technique for the time being. He continued other medical work and late in 1945 he published Chirurgie des pancréatites aigues (Surgery of Acute Pancreatitis) (Tùng, 1945).

During World War Two, Tùng focused on investigating ascaridiasis and his insights into the nature of the colonial situation evolved during these experiences. In his autobiography, Tùng lists the biological reasons for particular diseases related to the presence of intestinal worms noted in Vietnamese and other Asians. Ultimately, he concluded, among "the main reason[s] for the diseases caused by đũa worms (ascarid), phù tụy inflammation or đường mật gall stones, the largest part is due to the poverty of our working people." This realisation had political consequences for Tùng. He began to consider his ability to perform surgery of limited utility to the people of Vietnam. "The hardships of our people," he reasoned, "are because we suffer from the aggression and exploitation of imperialists, my ability to operate will not be able to save our people but the colonial exploitation must be abolished" (Tùng, 1978, p. 41). A life of science was not enough to cure the people; only the revolution could do so and Tùng enthusiastically joined the new Vietnamese government proclaimed by Hồ Chí Minh in August 1945.