No. Cows do not start producing milk until after they have given birth to their calves. Until that time, they are called heifers. When heifers reach the age of 2-2.5 years, they are then mature enough to produce their young.
A cow carries her unborn young for 283 days. This is called the gestation period. After birth, the newborn calf stays with its mother for its first eighteen hours of life, and is then taken away. But the mother’s milk is necessary for the calf to survive, so the cow is milked and the calf is quickly taught to drink that milk from a bucket. The milk that the cow produces for the first three or four days is not good for humans to drink, but it is nourishing for her calf.
After those first few days and for the next ten months, the cow produces milk which is good for people to drink. Then her milk supply dries up for two months, after which another calf is usually born, for cows usually calve, or give birth to young, every twelve months.
Because milk builds up rapidly during the day and night for those ten months, cows have to be milked every morning and evening.
Milking a cow by hand or machine increases the amount of milk she produces far beyond what she would have produced if she had continued nursing her calf!