On consoles, once the game is fully downloaded and installed on your platform, you do not need Internet connection to play the game itself (as long as the account that purchased this content has been activated to your console via Activate as Primary PS4 or My Home Xbox). However, some secondary features will be affected such as community and friends statistics or trophies/achievements…
On Xbox One, please note that it is strongly advised to wait for the complete installation prior playing, to avoid any potential graphical artifacts.
On the Epic Games Store, an internet connection is required at all time for the moment.