Adan was born into a Jewish family on in Kfar Giladi, British Mandatory Palestine; he was born with the surname "Eidelson", but later changed it to "Adan" as part of a Hebraization process. In 1943, he joined the Palmach, an elite force of the Haganah paramilitary organization that operated on part of the Yishuv community in British Palestine. During the First Arab–Israeli War, Adan was a company commander in the 8th battalion of the Negev Brigade, and participated in Operation Uvda, in which the brigade successfully captured the Jordanian-held outpost of Umm al-Rashrash—now known as Eilat—at the southernmost tip of the newly-created country. Adan, then a captain in the newly-formed Israel Defense Forces (IDF), was photographed while raising the Ink Flag of the State of Israel at the site. The photograph has since become an icon, and has been compared to "Raising the Flag on Iwo Jima", an iconic photograph in which six United States Marines are raising the American flag atop Mount Suribachi during the Battle of Iwo Jima in World War II.