The first recorded use of the phrase 'bite the bullet' - in the sense of meaning to accept something unpleasant and unavoidable with courage – came 34 years after the 1857 'Indian Mutiny', in a book called 'the Light that Failed' by Rudyard Kipling. Kipling was himself born and raised in India and had a very close affinity - albeit a colonial one - with India and its people.
The phrase 'bite the bullet' is commonly believed to originate from the days before anaesthetic was widely available for battlefield surgery and soldiers were given something to bite on, to cope with the pain of an operation. However there are those who believe that the phrase actually originates from the time of the Indian Mutiny, when the Gurkhas of the time (along with their Sikh comrades) cast aside their own religious practices when loading their newly-issued Pattern 53 Enfield rifles - by biting open the grease paper-wrapped gunpowder cartridges - despite the fact that the grease was made from pork and beef fat. Many of the native Indian Hindu and Muslim sepoys (soldiers), understandably, refused on the grounds that this would be sacrilegious - cows are sacred to Hindus and pigs 'haram', or unclean, to Muslims. This design fault is said to be what sparked the 1857 Indian Mutiny.
It is pure speculation, but if this is the case and Kipling's phrase originates from India, then the Gurkhas of 1857 could be said to be the first people to 'bite the bullet'.