But if that were the case, it would disconnect from our POV as Finn since he appears to believe that Poe went down with the ship.
The other films and the third act elevate Poe to a POV character anyway, so following him earlier in the movie isn’t a big deal.
You could potentially rework scenes from the Resistance base on D’Qar, including the deleted scene where someone asks “any word from Poe”, and you could engineer a new reply of “we found him” or something.