Rich was educated at Eton and graduated from Emmanuel College, Cambridge in 1603. Reportedly a godson of Henry IV of France, he travelled to Paris in 1607 before returning to England in 1610. Elected as MP for the vacant seat of Leicester in May, he was knighted in June when James I's heir Henry was created Prince of Wales. Shortly thereafter, he served as a volunteer in the Siege of Jülich (1610), part of the War of the Jülich Succession which preceded the wider conflict of the Thirty Years War.