He is/ was the first guardian or "risen" to be created. If there has always has been a speaker and the risen were created after the collapse it's safe to assume the speaker was the very first of his kind AND he holds the soul of the traveler. This "speaker" has always existed and has the ability to commune with the traveler yet we don't know how he got this power to talk to a dead god. The god (or traveler) is not dead but merely he changed forms and is now the speaker. The traveler was the first ghost so-to-speak and his choice was this form (referring to the speaker) and he imbued this form with his soul. This is why there has always been a speaker because the speaker was the first risen and the speaker IS the traveler.
Any feedback would be great!
Edit- 1) read the tags I put theory in there for a reason
2) I know this has no basis but is still a cool idea that I thought up. Most likely isn't true but still a cool idea.
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The Speaker very well could be the first Guardian, you're right about that. We do know is is not the reincarnation of the Traveler, and does not have its "soul" in him. However, it's been said that he receives visions from the Traveler (explaining the Dreams of Alpha Lupi) and his Light is strong. He also has a strong connecting with Ghosts and other Guardians, clearly because of his kind nature and Light, as stated by his grimoire. The Traveler was not the first Ghost, but did create the Ghosts. The Speaker has a caring nature identical to what we know the Traveler's to be, and because of his close bond to it he was chosen to represent it when the City leaders make decisions