If I've just had a baby, can I get pregnant before having my first post-baby period?

YES. Yes that can and does happen. It is not common. It means that the first month you ovulate you have sex and become pregnant. If you are breast feeding it is less likely to occur right away since you are probably not ovulating. But after your delivery you should definitely consider your plans for future pregnancy and contraception.
Yes. Ovulation can occur after a baby is born and allow for conception prior to a first period.