Juozas was born on 20 November 1904. There were eleven children in the family. During his childhood, he had to help his parents with various farm work.

He attended the Marijoniai Gymnasium in Marijampolė, where he graduated from 4 classes with honours. Later he went to study at the Lyceum in Turin, Italy. He returned to Lithuania and in 1943 graduated from the Faculty of Humanities of Vilnius University with a diploma in classical languages. After the war, he worked as the headmaster of the Vilkaviškis Gymnasium, a teacher in Kaišiadorys, and an education inspector. Later he was not allowed to work in the field of education, so Juozas Paukštys chose the profession of an economist and accountant. He has written articles on various philosophical and theological issues.

Juozas' wife Stanislava (1914-2001) worked as a midwife. The family had a daughter Jūratė in 1940 and a son Skirmantas Juozas in 1950, both of whom chose medical professions. 

During the Holocaust, Juozas Paukštys hid Jews in his house.

From the book of memories published by his son Skirmantas Juozas, MES (We) :

"What are the most important character traits of my father? Temperance, self-confidence, elegance, straightforwardness, honesty...

...A very important trait is dignity, maintaining one's own worth.

...Father was well aware of the danger he was in, but to help a man in distress was a duty of the heart.

...Father was able to keep the details of everyday life simple and had a subtle sense of humour."