I have found 5 baptism entries of a John Norman within 20 miles of Keymer which is where he married Mary Hayward in 1769.

These are

• 1728 &1730 at Henfield (both with parents John & Susan so the earlier child must have died)
• 1731 (1732 on the modern calendar) at Horsham
• 1736 at Isfield    and
• 1736 (1737 on the modern calendar) at Glynde

The nearest is Henfield (8 miles from Keymer) but that is not sufficient to be confident that it is the right choice so I am leaving it open until any further evidence comes to light.