In many Bethesda-publisher games, such as Dishonored and Skyrim, you can move your head during cutscenes. Sometimes, the camera pulls you in a certain direction, like with the cutscenes with the Outsider in Dishonored 2, and sometimes you can almost fully move your head while stuff happen, e.g. while a boat your in moves. Other than in some of the Bethesda games I’ve played, you can do this in BioShock. What is the first game to have cutscenes in first-person where you can rotate the camera but otherwise can’t move?
I remember that Half Life was hailed as the very first game where it does not cut the camera away from the First Person Perspective to do a cutscene (and pretty much no breaking the first person camera for the whole game). So I would guess that is the answer to your question.
Can't find an article that says exactly what I'm saying but here is the closest I've got from a Guardian article
The brilliance of Half-Life begins with its immersive storytelling. The opening accustoms us to the Black Mesa research facility, tells us a little about Freeman’s role and sets up the narrative universe – all without leaving his perspective.