Rudyard Kipling wrote a terrific short story about this.
Rikki-Tikki-Tavi
Hopefully, it can be found online You would enjoy it.
It’s not something that anybody “started”. Fighting a snake is a natural instinctual behavior for a Mongoose. They are ancient enemies.
But similar to the way the Egyptians discovered that domesticating cats to hunt mice resulted in fewer losses in their granary storage, people likewise found having a Mongoose around gave them protection from death from poisonous snakes creeping into their homes unawares.
Obviously those who made the most notable use of these were the British when they began to colonize India.
That’s where Kiplings story takes place and I’m sure that his excellent writing skills helped to popularize the Mongoose worldwide.