Earliest Possible Time Frame. It is possible to get pregnant during the first month after giving birth. According to general practitioner, Dr. Louise Newson, pregnancy can occur from the time your baby is 21 days old -- just three weeks after delivery.The first postpartum egg is generally released before the first postpartum period.arliest Possible Time Frame. It is possible to get pregnant during the first month after giving birth. According to general practitioner, Dr. Louise Newson, pregnancy can occur from the time your baby is 21 days old -- just three weeks after delivery.