Rogue isn't a starting class, but can be unlocked once you unlock the Armory System that allows adding additional classes. That in turn is available once reaching level 10 in your starting class.

If you want to unlock it immediately at 10, you should start with one of the classes that begins in Limsa Lominsa, so that means either Marauder or Arcanist. If you start with any other class, then you'll have the additional requirement of unlocking airship travel so that you can reach Limsa Lominsa. That comes in at level 15 in the Main Scenario quests.

Once you have completed your first class's level 10 quest and are in Limsa, pick up the So You Want to Be a Rogue quest in Limsa Lominsa's Lower Decks. That in turn leads to My First Daggers which actually unlocks the class.

Once it's unlocked, switching classes is just a matter of equipping different weapons. Whenever you have Rogue daggers equipped, you're a Rogue.

When you have more than one class unlocked, each has its own level. So, for instance, if you started as Marauder, took it to level 10, and then unlocked Rogue, you'd then be a level 1 Rogue when you equip daggers or a level 10 Marauder when you equip an axe.

Since some gear is restricted to only certain classes and most gear is restricted to having a certain minimum level before you can equip it, each of your classes will also have different armour/jewelry you'll want to equip along with the weapon. To enable this, the game lets you assign groups of gear to Gear Sets, so instead of just equipping your daggers, axe, or whatever to change classes, you'll equip your Rogue Gear Set, Marauder Gear Set, or whatever, changing all your gear at once. There will be a tutorial window pop up when you unlock the Armory System explaining how to set these up.