Can you start pumping breast milk before your baby is born? at 36 weeks?

No: Milk doesn't come in until 2-3 days after the baby is born.

Pump before delivery: It can be done but if you start to pump your breasts before the baby is born, there is a chance that you will precipitate the delivery before the baby is ready. Also, a newborn breastfeeds and your body naturally produces oxytocin to help your uterus “clamp down” after delivery. This action helps to tone your uterus and bring it back to the normal pre-pregnancy size.

Not recommended: I wouldn't recommend it. Breast/nipple stimulation will make you have contractions and could put you into pre-term labor. Also, your milk usually doesn't come in until after you give birth. Best Wishes!

No textbook answer: I am not aware that there is a textbook answer to this question. What is known, is that stimulating the nipples for example by pumping is likely to start uterine contractions. There is no way to be sure that these contractions will not dilate the cervix and set the woman on the path for delivery. If the leakage is bothersome I would try wearing a tight bra and cooling the breasts with ice packs.