Neville Wilmer was born in Townsville on 17 August 1918. He attended several state schools across North Queensland and was a border at All Souls School, Charters Towers, before studying medicine at the University of Queensland in Brisbane. During his undergraduate days, he excelled in swimming, boxing and rugby.

After graduating in 1941, Neville worked as a Resident Medical Officer at the Royal Brisbane Hospital (RBH), then joined the Army and served with the 7th Division in Papua New Guinea. In 1945, he was sent to Timor to participate in the Japanese surrender.