Just bought a PS4 in order to play Gran Turismo Sport. My first console since playing GT3 on PS2 15 years ago. I've got some questions...

I literally haven't owned a console in the modern era of online gaming. Simply having online functionalities is blowing my mind. However, when I booted up the game, even after making sure my PS4 is connected to the internet, I got the "your game will not be saved in offline mode" notice and the only thing I can do is play basic Arcade single player races. What am I missing? How do I unlock the rest of the game? Sorry for such painfully noob questions...