I am completely new to League of Legends, but as far as I understand, the only ways you can play a champion are by buying it, renting it with the crafting system, or playing it when it is part of the free rotation. However, as you can see in the picture below, when I select my champion at the beginning of a game, only one of the free rotation champions is available, and several other champions that I have not purchased or rented are available. Why is this?
Good afternoon Arti Schmidt!
League of Legends has a different system for new players, which means in the first few (5 if it is still the same) levels you will have a specific champion rotation available. After those levels you will have the normal free rotation. You can read more details here: League of Legends Starter Champions - Article at RockPaperShotgun or here: League of Legends FAQ (almost at the bottom of the page).
Best wishes, I hope I could help!