The time it takes to grow a mustache depends on how fast the hair grows and the type of mustache desired. On average, hair on the body, including the face, grows at a rate of 1/2-inch per month.
Unfortunately, there is no way to make hair grow faster or thicker, despite the numerous products on the market that make that claim. Facial hair naturally grows thicker and faster with age. For some individuals, the hair growth rate and thickness might slow with advanced age.
Shaving the hair will not encourage it to grow any faster or fuller. Hair is made of keratin and protein without a blood supply or nerve endings, so growing it or shaving it isn't transmitted as a signal to the body to produce more hair.