Quite possible. Deictic reference (words that refer to people or places related to some universal viewpoint, usually the speaker) is central, very commonly used function of the human language. It would make sense that the language started with the desire to express these kind of relations.

Of course, there is no way to prove it as we have no way of knowing what the earliest languages looked like. I’m sure however it had a word that sounded something like “ma” or “pa” and referred to a close person or group of people.