Maybe the speaker is the "Spinner of the Years" that the poem refers to, since he (and we're just assuming it's a he) uses such an omniscient point of view in "The Convergence of the Twain." Those might be some tough shoes to fill, but the speaker definitely has the kind of perspective that sees all, whether at the bottom of the sea or in the midst of the Titanic's construction. It's almost like he sees everything during and even before it's about to happen, especially when he talks about the "later history" that would become the Titanic's story. (This would be a good guy to know for betting on sports…)
And since he uses such a rhythmic voice that mimics the sound of the tide, we might even feel like he's part of the aquatic world we visit, which makes him sound even more omniscient. He's no stranger to those "dim moon-eyes" that wonder what that hunk of metal is doing at the bottom of the sea. He's also no stranger to man's vanity since he's able to really hone our attention to the sorts of useless things people occupy their time with. But he's not getting all preachy about it or anything. He's just an observer here with a pretty keen eye for all things Titanic, whether we're talking about the actual construction or its later destruction.
The thing that keeps his voice grounded despite all the omniscient stuff is the passive voice he uses. He tells his story after everything has already happened, so although he might have anticipated that which "no mortal eye could see," we can't forget that we're hearing it all in retrospect. So he may sound clairvoyant, but he isn't. At the end of the day, he's just like one of us witnessing a tragedy and trying to put all the pieces together in a way that makes sense.