For me it's a surprise that babies articulate a double-syllable word do express pain, while pain is something spontaneous, and I guess it would be expressed by a single-syllable, or single vowel. So I asked somebody:
I had a conversation with a friend, who claims that aua! is completely natural, and isn't taught by the parents (tutors, nanny, older siblings or similar influence). I doubt it. If it were natural, then lot of babies in the world would say aua! when something hurts, and not only those of German speaking parents. (I even doubt babies' first word is mama because of easiness of the word, but because the mother expects the baby to say this and repeats him that word – I might be plain wrong, though).
Now, the parents don't say aua! when something hurts, but they expect the baby to say aua! when they read pain in the face of the baby (I guess), so they fake the aua! a baby is expected to do. So I guess the interjection is said by the babies only because the parents transmit it, isn't it? Does anybody have evidence showing the contrary?