The conclusion is inescapable. The mama/papa words are not fossilized relics of some ancient ancestral language at all. Instead, they are being created all the time. New examples of mama/papa words are constantly being invented and passing into use. At first these new words survive alongside the older ones as informal or intimate versions, but eventually they may take over completely and drive the older words out of the language.
The new examples, it is hypothesised, come from the sound babies make during their babbling phase. A babbling infant isn't trying to speak, but rather calibrating its vocal chords, though that doesn't prevent the proud parents from picking out its sounds and adopting them as informal terms for "mother" and "father" (and occasionally other things in the environment, such as older siblings or relatives; such words for younger siblings are conspicuously absent, as the theory would predict). The word sticks, and the child grows up calling its mother "mama" or similar. These new-formed words fall onto the conveyor belt of language, gradually fossilise into more formal forms, and ultimately fall into disuse as newer, fresher words take their place.