Perhaps it is the power of suggestion at work here. At that stage of development, the infant typically does not have to ability to form words. Many researchers have suggested that our larynx and vocal cords- responsible for reproducing sound- do not fully develop until adolescence. It is because of this that I do not believe the child is actually saying anything at all.
Many first-time mothers are extremely eager to witness their child acknowledge the role they play in his or her life. Therefore, the power of suggestion might influence the comprehension of these "babbles", turning something entirely incomprehensible into a form of endearment. That is most likely why some people- when witnessing another child's first "word"- do not understand what they are supposed to be hearing according to the parents.
I am not sure of the origins of "mom" or "dad", but every culture possesses it own variations of these terms. Several languages have similar variations and others are completely different. I would chalk this up to cultural differences, especially when discussing the origins of slang.