Ransom was born in Norwich, Vermont, son of Colonel Truman B. Ransom, who was killed in action at the Battle of Chapultepec during the Mexican–American War, when the younger Ransom was only 14 years old. The father was remembered by a participant in that battle, Adjutant General Richard Coulter Drum of the Regular Army, as "by all odds the most brilliant man under fire I have ever seen." His son, Thomas, entered Norwich University in 1848, where he remained three years. After graduating in 1851 he went to Illinois, where he engaged in civil engineering and real estate speculation. He initially lived with his uncle, George Gilson, then mayor of Peru, an Illinois River town in LaSalle County. Ransom was known as the "boy surveyor" of LaSalle County. During that period, he was joined by his close friend and fellow Norwich University graduate, Grenville M. Dodge, who would later win fame as a Civil War general and the chief engineer of the Union Pacific Railroad.