It generally takes months. It's not like women can lactate just by pushing their nipples either.

In the ordinary course of events, they need to get pregnant, build up all the ducts and milk producing cells, and then get the right combination of hormones to trigger milk production. And then you have to keep removing that milk, or it stops.

You can get people not going through pregnancy to lactate by giving them the hormones. Recovery from famine can also produce the needed hormone spike.