Thomas was born as Thomas Henshall. When Thomas was ten, his father died and his mother remarried to William Griffin, and Thomas adopted his last name.
At the age of 14, Thomas began an apprenticeship as a mechanic and tool maker to John Sutton Nettleford. Soon after his internship was over, he was converted to the Church of Jesus Christ of Latter-day Saints in 1849. He left England on Feb 9, 1854 and joined the William Burton Company. They sailed on the Windermere and landed in New Orleans, Louisiana on April 23. Thomas joined the Job Smith Company on June 7, 1854 and arrived in the Salt Lake Valley on Sep 23.
For work, Thomas did what he could, including working as a mortar. Thomas married Amanda Ellen Perkins on Oct 19, 1856 in Salt Lake City, Utah. After the conflict of the Utah War, the Griffin family moved to Richmond in 1860.