Hamilton was probably born in Strabane, County Tyrone, Ulster, near the Dunnalong (or Donalong) estate, which was his father's share of the land granted to his grandfather Abercorn during the Plantation of Ulster. His uncle Claud had lived in the Castle of Strabane until his death in 1638. The family probably fled before Phelim O'Neill burned the Castle of Strabane in 1641 during the Rebellion and took his aunt Jean, Claud's widow, prisoner.