They say you only need to connect to the internet the very first time in order to authenticate the game. However, I will say (in fairness) that if you FIRST login when CONNECTED to the internet, select 'offline mode' but keep Origin running, then disconnect from the internet, the game will launch. The Sims 4 ABSOLUTELY is not playable if you're not connected to the internet. Closing the Origin Login box did nothing except close the program. It just sat there and the game didn't launch. The Origin Login box popped up and said 'Online login is currently unavailable'. I then double-clicked The Sims 4 shortcut, which launched Origin. I decided I wanted to test the offline capabilities so I unplugged my ethernet cable from my router, disconnecting my computer from the internet. I then quit the game, which closed both the game and Origin.
I double-clicked the Sims 4 shortcut to launch the game, and this automatically launched Origin and logged me in (I had it set to auto-login). To test this, I had Origin Advanced Settings to 'Automatic Exit' when I quit the game. EA says the game doesn't require an internet connection, and that is also incorrect.