Although, unfortunately, the designers made the Raven look like a Starfleet ship. Maybe it was a decommissioned one that was now in civilian use.
Jacques Cousteau's ship, the Calypso, began it's life as a French Navy mine sweeper.
Oh, don't get me wrong. I'm not saying the science teams would have to be Starfleet. But the crew operating the ship would be.
I don't follow, why would they have to be Starfleet?
I was watching an old documentary resently on how Robert Ballard found the RMS Titanic, the research ship wasn't being operated by military personnel or government employees. The Woods Hole Oceanographic Institution is a private, nonprofit research and higher education facility.
Having the next Star Trek series starship operated by a similar organization would be one possibility.