Introduced 1000 BCE.
"The origins of Shinto are clouded in the mists of the prehistory of Japan, and it has no founder, no official sacred scriptures, and no fixture system of doctrine." (1)
The first evidence of human presence on the Japanese islands dates from 1000 BCE (2), so this could be considered the 'start date' of Shinto.
1. 'Shinto' in The Oxford Dictionary of World Religions, ed. by John Bowker (Oxford: Oxford University Press, 1997).
2. World Religions: A Historical Approach (4th ed.), S. A. Nigosian (Boston: Beford / St. Martin's, 2008), p.273.