On the original PS5, yes.

On the PS5 refresh, no, an internet connection is required to activate the drive, whether or not it came in the box.

On the Xbox One... you haven't been able to, for over a decade.

On Switch... Switch is just delightful. The game cards even come with the required system updates (criticism for lack of theming or music aside, the whole OS is under 400MB, so amazing things are possible). You can also update your game or system wirelessly, from any other Switch, which has a higher version of either, no internet necessary.