According to Deane and the Hingham history, he was in Hingham, Massachusetts by 1637. This is not likely, because he would have been about ten years old. Anderson puts the birth date for Thomas Turner, son of Humphrey and Lydia (Gaymer) Turner, at about 1627. Thomas was younger than John Turner, the eldest son, who was baptized in Terling, Essex, England, 24 March 1621. Their parent's marriage record is found in the nearby parish of Sandon, Essex, 24 Oct 1618. 
According to the Hingham history, "Thomas, had a grant of land in Hingham at 'Goose Point,' 1637. On Apr. 13, 1646, he sold his est. here, consisting of five acres of land with a dw. house thereon, which was located where St. Paul's Catholic Church now stands, to John Otis, Sr., together with two acres in the Broad Cove meadows, and twelve acres beyond Crooked Meadow Bridge, which has previously been granted and laid out to him by the town. In 1659 he complete a contract for finishing a 'barke' at Boston, and prob. removed from here about that time, or shortly after. In 1644 a Thomas Turner was one of four young men who were permitted to build a gallery in the first meeting-house, but whether it was this Thomas or his s[on] is a problem for investigation. Deane's history [of Scituate] says the name aft[erward]s appears in Scit[uate]." [1, 2, 3]
Thomas Turner married Sarah Hiland in Scituate, Massachusetts 6 Jan 1651/2. Thomas is named in the will of his father, Humphrey Turner, "to my son Thomas Turner all my wearing clothes, one wood bed and blankets". 
Humphrey Turner is said by Anderson to have immigrated by 1632, first to Plymouth, and removed to Scituate by 1634, with his wife and children. 
↑ 1.01.11.21.3The Great Migration Begins: Immigrants to New England 1620-1633, Volumes I-III, by Robert Charles Anderson, pages 1844-5
↑ 2.02.1Lydia Gaymer, the Wife of Humphrey Turner of Scituate, by Vernon Dow Turner, NEHGR Vol 151 (1997), page 287
The Great Migration Begins: Immigrants to New England 1620-1633, Volumes I-III. (Online database: AmericanAncestors.org, New England Historic Genealogical Society, 2010), (Originally Published as: New England Historic Genealogical Society. Robert Charles Anderson, The Great Migration Begins: Immigrants to New England 1620-1633, Volumes I-III, 3 vols., 1995). Humphrey Turner's children, page 1844-5
Lydia Gaymer, the Wife of Humphrey Turner of Scituate, Vernon Dow Turner, NEHGR Vol 151 (1997), pages 286 - 290. Repository: The New England Historical and Genealogical Register. Boston, MA: New England Historic Genealogical Society, 1847-. (Online database: AmericanAncestors.org, New England Historic Genealogical Society, 2001-2013.)
1. [S560] History of Scituate, Massachusetts, from its First Settlement to 1831, Samuel Deane, (Boston: James Loring), 363.
2. [S366] History of the Town of Hingham, Massachusetts, George Lincoln, et al., (Hingham: Town of Hingham, 1893), 1.202.
3. [S366] History of the Town of Hingham, Massachusetts, George Lincoln, et al., (Hingham: Town of Hingham, 1893), 3.270.