I think, we have enough hints about his position as first officer: Fact: He is definitely highest ranking Starfleet officer after NX-01 after Archer with existing crew. - Not only discussion at Decon chamber, but as they begun to verbal fight at bridge reaction of other senior officers confirms it. -There is also a deleted scene which shows Travis didn't follow T'Pol's order without Trip's authorization. Theory: There maybe someone existing who couldn't join the crew before this "emergency mission" - At the end of the Broken Bow, there is no reason, not back to home (or Jupiter Station) for picking him/her up. Whole distance is only four days ( ) to the earth. -Nevertheless, they get the order from Star fleet to continue their mission. -At that moment no one knows, if T'Pol stays with them. Clear, Archer should have tell his idea to his superiors, but they didn't know what would be her decision. -For a second, let me think, Trip was only compromise for the moment, so Archer needed 3 days to prepare the NX-01 for the initial flight plus they needed 8 days to Qo'nos round trip. Qo'nos is 90 lightyears away from Earth. As Suliban abducted Klaang, they were 15 lightyears away from Rigel X, then they needed +2 days and if we add a day for Suliban cell complex adventure we could say Star fleet had ca. two weeks to find someone as first officer. Have they done? No. So, Star fleet sees no necessity to add someone to the existing crew (even without T'Pol) in theory or in practice. Conclusion: It would be a interesting twist, if we had a first officer who is left behind with broken heart. But it is highly unlikely that we had one. And that is a good thing to have one less unhappy person on the Earth.