I am from India and always have between cows and buffaloes. Remember, my description of dairy will be different from Industrial dairy.

So, we used to have 4 to 5 cows. Whenever a cow gives birth, we will always feed the baby first. New born babies get almost half of milk and rest will be used by family. As the calf gets older like 3 months, the milk consumption decreases and he will eat food such as grass and feed.

after some time they grow old enough to completely feed off the grass. this is when family can use all the milk. Cow will keep giving milk up until 2 years on average and they may become pregnant. However, the quantity will keep decreasing overtime and fat percentage will increase.

Cows start the milk process for the first time when they give birth.