It has been postulated variably through the study of language through to a proto-Indo-European, that language may have arisen either from one single source, or else independently in multiple locations. But whether there was a single original or more than one I doubt that we could ever possibly know. At every instance of history I've looked at there was remarkable movement between different geographic areas, of goods and ideas. Take the spread of farming, for example, which although apparently developed independently in a handful of areas - Mesopotamia managed to pass it on across Europe and Asia. So if language ever developed independently there can be little doubt that linguistic mixing occured early on and frequently since - both through the movement of trade and through the passing of innovative ideas. Quite possibly, there was never a single well-formed language to originate from, but instead a "soup" that was further developed into full language in different areas.