TBI encompasses a wide spectrum, from the very mild to the fatal injuries. So your question does not have a blanket answer.
Most witnessed/documented TBIs get seen in the ER first, at a Level 1 or 2 center, during the acute phase. After initial evaluation in the ER, and based on findings of physical exam, imaging, and associated injuries, as well as specialty service available, the neurosurgical (or general surgery or orthopedics if no neurosurgery on site) team is consulted, and further management planned. The management phase of moderate to severe TBI involves multiple specialties from neurosurgery, other surgical specialties in case of other injuries, to physiotherapists, rehabilitation teams, social workers, neuropsychologists, etc.
Mild TBIs, if they get seen in a timely fashion, get discharged with no clear cut guidelines for further follow-up-it is very location/center dependent. Mild TBI has now proved to be not so mild after all as it has long term damaging neuro-cognitive sequelae. That's why it is the new silent epidemic raging the country, rather the world, but that's a whole 'nother story.
80% of TBIs are mild. When these patients start developing neuro-cognitive deficits a year or so down the line after their "mild" TBI, the association is not made, as most of the time people don't even get seen by any medical personnel. Hence the initial referral by a family physician might be to a neurologist to evaluate the patients for any neuro-degenerative diseases.
So, to come back to your question, AFAIK, there is no "must see", and everything depends on patient presentation. As always, I am open to read/learn what others have experienced.