"In linguistics, mama and papa are considered a special case of false cognates. In many languages of the world, sequences of sounds similar to /mama/ and /papa/ mean "mother" and "father", usually but not always in that order."
Quite confusing, but it seems to work?
consider all the sounds humans can produce
now ask yourself
1) amongst them, if p and d are close (there is no world in which the answer to that is "no")
2) if there are real life examples of languages shifting between them or using them interchangeably (there are, papa and dada being a prime example)
I'm not sure we can conclude that? Borrowings can displace existing words, so the current state of the vocabulary doesn't necessarily tell you what was there before.
As a slightly related example in German: 'Base' and 'Vetter' for your girl and boy cousins have been replaced in the last few decades with the French borrowings 'Cousine' (also spelled 'Kusine') and 'Cousin' (also spelled 'Kuseng'). Looking just at the current vocabulary, you might conclude that German did not have specific words for these people until the French come along.
Germans also replaced 'Muhme' and 'Oheim' with 'Tante' and 'Onkel'.
Fun aside: the English word 'boss' has etymological ties with the German 'Base'. (English got 'boss' from Dutch.)
No idea where that came from, but we understood pretty quickly.