Dragon Ball Z: Kakarot takes you through the main story beats of the anime series, Dragon Ball Z. Although the name of the main character, Goku, also known as Kakarot, is in the title, you can also play with several other characters from the series. A great antagonist, then later protagonist, is Vegeta, the prince of all Saiyans.
During the Namek Saga, you have your first chance to play as Vegeta. He bypasses a handful of Freiza's crucial henchmen before he, Krillin, and Gohan have to confront the Ginyu Force. At this point, you can play it a little more often, but overall the game restricts who you can play based on what major story moments you can play as.
Unfortunately, that's the big deal in Dragon Ball Z: Kakarot. During story missions and some parts of the game, you won't always have the option to choose someone to play like during gameplay. You should automatically play as a specific character depending on your point in the story . However, there are certain parts where you can choose different characters, such as during intermissions between sagas.
For Vegeta, he becomes openly available to you as a major character following the Freiza saga. After this point, be sure to check your party options in the main menu to switch to him if you're in the middle of an intermission. You can upgrade him, activate his super attacks and make him a powerful ally. The same goes for every character in the game.