Its just about impossible to date and credit the creation of hockey. Field hockey predates bandy (an on ice version) which predates hockey as we know it. Bandy, the closest thing that could be considered the origin of hockey, has been recorded in Russia as early as the 11th century.
Even in Mongolia, for what it is worth, a tradition of beating dung with a stick across the frozen steppes while herding livestock, has been boasted as the ancestry of modern hockey.
Early settler accounts in lower Canada have documented natives playing an on ice game with sticks, a ball and net in a famous poem, the name of which escapes me now. Supporting this is the carbon dating of a hockey stick type piece of equipment found in Eastern Canada and now held by a Quebec collector. That stick, it is said, dates back to the 1600's.
That being said the OP may a slight argument as the first accounts of hockey in Canada date back to the 1840's or so and it being played at a British military post in Halifax.
Further credence is given to this theory by the fact that hockey in Canada was originally played on bone skates, which as best I know would have been introduced by the Dutch via British settlers.
As for the Russian version above, I have not read any account of skates being used, which I would argue is a defining component of modern hockey.
All and all it is an extremely difficult origin to date and an even more difficult argument to prove. I would say however that when the athletic department at McGill officially documented the rules of the game they called hockey and played that first game on March 3rd 1876, the modern game of ice hockey separated itself from all other forms of the sport and was thus born.
As an aside, officially, the oldest hockey stick in Canada originated in Nova Scotia and dates back to 1852. It just sold for 2.2 M and is on display at the hhof.