Young was born in 1741 at Whitehall, London, the second son of Anna Lucretia Coussmaker, and her husband Arthur Young, who was rector of Bradfield Combust in Suffolk and chaplain to Arthur Onslow. After attending school at Lavenham from 1748, he was in 1758 placed at Messrs Robertson, a mercantile house in King's Lynn. His sister Elizabeth Mary, who married John Thomlinson in 1758, died the next year, which disrupted the plan for Young to work at Messrs Thomlinson in London, under his sisters in-law.