McLaren is named after Bruce McLaren, the New Zealand racer who never won the Formula One World championship, but set up a team that has managed exactly that 12 times so far. As well as a driver, Bruce was also a gifted engineer, which means that the question of when McLaren started building road cars isnt quite so straight forward. 
1994 is the answer that makes most sense as that was when McLaren, under the guidance of Ron Dennis and Gordon Murray, released the production F1. Arguably the worlds first hypercar, the three-seater was revolutionary, but the first? Some 26 years earlier Bruce tried to homologate an M6A Can-Am racer for Le Mans. The project never materialised, but two road cars, badged M6GT, were made, one of which Bruce used as his daily driver until his death testing a McLaren M8D Can-Am car at Goodwood two years later in 1970. 
Neither the M6GT nor the F1 properly got McLaren going as a road car manufacturer. For that we had to wait until 2010, the unveiling of the MP4-12C and the creation of a much more diverse and extensive plan.