By Wond PregYes. Especially if you’ve already had children, you might notice that your milk comes in early or that you have occasional leakage, even in the first trimester. Even if you haven’t had a baby yet, it’s not uncommon at all for you to leak some milk. If this is a persistent problem (or an embarrassing one), you might need to change up your bra or wear nipple shields so that your nipples are less stimulated.