Both words have been used in English - in one form or another - since the 15th century. 'Mama/dada' are just reduplications of a sound that babies make instinctively. In the case of 'mama', it is used in virtually all countries where the proper word for 'mother' begins with the 'm' sound, as in French, German etc.
The actual form 'dad' is far older than the form 'mum', since the former has been around for half a millennium and the latter has existed only since the early 1800s. (As 'mam', however, it's been around for as long as 'dad'.)