YES, YOU CAN. So if you aren't ready to conceive while breastfeeding, it is best to use a reliable form of birth control as soon as you start having sex again after your baby's birth.
That said, it's true that you may not ovulate for several months (or even longer) after giving birth, especially if you're exclusively breastfeeding your baby. In fact, there is a contraceptive technique called the lactational amenorrhea method (LAM) that is based on the observation that breast milk production tends to delay the return of menstruation. But in order to use it properly, you must breastfeed at least every four hours during the day and every six hours at night, and not supplement breastfeeding with formula. If you do not do it right, do not expect to be protected. This method is 98% effective during the first six months after delivery when you follow the rules perfectly.
After six months, you could start ovulating again at any time without knowing it. Some nursing mothers do not menstruate until they stop breastfeeding. If this is the case with you, do not be deceived by the absence of menstruation as you may still start ovulating at any time. This is because your body is likely to release its first postpartum egg before you get your first period after delivery. So you may not know that you have ovulated until two weeks later when you menstruate or start feeling early signs of pregnancy.
Speak to a health practitioner or midwife about the family planning method available to you. It is advised that you seek family planning methods 6 weeks after childbirth. Family planning is free in most hospitals and very safe. Your health care provider will choose the best methods for you based on your lifestyle and your body.