Tidball was born near Wheeling, Virginia in Ohio County, Virginia (present-day West Virginia), to parents: James Squires Tidball and Maria Caldwell. He grew up on a farm in eastern Ohio. He graduated eleventh of thirty-eight cadets in the United States Military Academy Class of 1848, and entered the United States Army as a brevet second lieutenant in Battery E, 3rd U.S. Artillery. He was commissioned second lieutenant on February 14, 1849, when he was transferred to Battery M, 2nd U.S. Artillery. Promoted to first lieutenant on March 31, 1853, he transferred again to Battery B, 2nd U.S. Artillery. He served in the Third Seminole War fought against the indigenous Seminole tribe, and accompanied an exploring expedition to California in 1853–1854. In 1859 he was sent on the Army's expedition to Harper's Ferry, Virginia to suppress John Brown's raid.