Kosinski was born Jzef Lewinkopf to Jewish parents in Ldz, Poland. As a child during World War II, he lived in central Poland under a false identity, Jerzy Kosinski, which his father gave to him. Eugeniusz Okon, a Roman Catholic priest, issued him a forged baptismal certificate, and the Lewinkopf family survived the Holocaust thanks to local villagers who offered assistance to Polish Jews, often at great risk. (The penalty for helping Jews in Nazi-Germany-occupied Poland was death for all members of a family and sometimes for the inhabitants of the village).

Kosinski's father was assisted not only by town leaders and clergymen, but also by individuals such as Marianna Pasiowa, a member of an underground network that helped Jews evade capture. The family lived openly in Dabrowa Rzeczycka, near Stalowa Wola, and attended church in nearby Wola Rzeczycka, with the support of villagers in Kepa Rzeczycka. For a time, they were sheltered by a Catholic family in Rzeczyca Okragla. Jerzy even served as an altar boy in the local church