Yes, a baby can be born without kidneys, a condition called bilateral renal agenesis.
According to the provided reference, renal agenesis is a condition present at birth where one or both kidneys are absent. The kidneys usually develop between the 5th and 12th week of fetal life and start producing urine around the 13th week. Therefore, if the kidneys fail to develop during this crucial period, a baby can indeed be born without them.