Eventually of course it would fill, but not in the time frame depicted in the film.
The same physics are in play in a submerged car, if you were in a vehicle that ran off the road into a body of water, you should roll down or shatter the side window, allow the car to fill with water and then swing the door open. Attempting to push the door open from inside the dry car is useless.
Also, because the body is more or less neutrally buoyant, pulling open the door as you would on dry land doesn’t work either, you would need to pull the door handle while bracing the other hand on the safe body, otherwise you’ll just pull your body to the safe instead of the door to you.
