You can launch an Invite Only Session from the single player mode: select Options > Online > Invite Only Session. You can also choose to launch a Solo Session if you don't even plan to invite any friends to your game.
You won't be able to start GTA Online right from the get-go. That's because you'll need to complete the GTA single-player prologue first. Once you gain control of Franklin, you should be able to switch to GTA Online via the menu or by selecting it when launching the game.