Born to a Jewish couple in the Lithuanian city of Telšiai, Noyk moved to Dublin with his family when he was one year old.
He was educated at Dublin's The High School and then entered its Trinity College as a sizar in Hebrew, before winning a classics scholarship and graduating in 1907.
He joined Sinn Féin shortly after the Easter Rising and was responsible for defending a number of IRA prisoners including Sean MacEoin, Thomas Whelan, Patrick Moran, James Boyce, and Frank Teeling.
During the Irish War of Independence, he was a high-level official and adviser with the Department of Finance which was then headed by Michael Collins.
He was responsible for the procurement of offices at 22 Mary Street in Dublin where the First Dáil's Department of Finance was located during the war.