Very rarely, especially in the side games/non mainstream Games, you aren't given the Opportunity to choose who your first Pokemon are. Oftentimes, your starter Pokemon are predetermined OR you do in fact get to choose who your first Pokemon is, but it AIN'T a starter Pokemon.

I am NOT including games where you don't get a Pokemon at all such as Pokemon Snap or Pokepark.

Here are some games Pokemon has put out where you DONT Get to choose your Starter Pokemon/Your Starter Pokemon AIN'T a starter.

1. Pokemon Colosseum

Pokemon Colosseum is the first Pokemon game in existence to break tradition and not even allow the player to pick out their starter Pokemon as instead Wes, the Main Character, is introduced to the player as a seasoned trainer as he already has two well trained Pokemon under his wing. Yes, the Pokemon you start out Colosseum with are Level 25 Espeon & Umbreon. Espeon is one of the best Pokemon in the entire game therefore the game gives you a vital asset right out of the gate. To be fair, the second Pokemon you're allowed to capture after a Makuhita is your choice of the Johto Starters in their mid stage: Bayleef, Croconaw or Quilava. However, while you do eventually get access to starter Pokemon, you start out the game with predetermined Pokemon.

2. Pokemon XD Gale Of Darkness

In Pokemon Colosseum's sequel, Pokemon XD Gale Of Darkness, the player is introduced to a teenage boy named Michael. Michael is the player character and much like Wes of Pokemon Colosseum, Michael already has his own already trained Pokemon. Michael's 'Starter' Pokemon is a Level 15 Eevee that belonged to his late father. Very very shortly into the game, Michael is given the opportunity to Evolve his Eevee into literally any Eeveelution that existed at the time, those being Jolteon, Flareon, Vaporeon, Espeon or Umbreon. This is the ONLY game by the way in which Eevee can evolve into Espeon or Umbreon through evolution stones. So 100% the player is given the choice of which Eeveelution they want as a starter Pokemon.

3. Pokemon Ranger

In the First Pokemon Ranger, the Player Character isn't given a choice of their Starter/Partner Pokemon. Depending on which gender you choose to make the player at the beginning of the game determines which Partner Pokemon you obtain. If you choose the Female Character, she is given a Plusle as her Partner. If you choose the Male Character, he is given a Minun. Your Partner Pokemon in this game is only used in order to recharge your Capture Stylus, therefore it isn't exactly useful in battle as it can't help in capturing targets, but Plusle and Minun are adorable and welcomed travel companions and act as mascots for the game.

4. Pokemon Ranger Shadows of Almia

In the 2nd Outing for the Pokemon Ranger games, you once again don't have traditional starter Pokemon BUT you actually get a choice of which Pokemon becomes your Partner Pokemon. After helping an old lady round up her Pokemon, to thank you, she heavily encourages that the Player takes one of her Pokemon out for an adventure. The three Pokemon in question are Pachirishu, Starly & Munchlax. As the game progresses, you can take on optional quests where more Partner Pokemon progressively become available such as Cranidos, Gible, Sneasle or Misdreavus. So yeah, while this game does allow the player the choice of which Pokemon they'd like as their first, they still aren't traditional Starter Pokemon.

5. Pokemon Legends Arceus

Okay so technically Rowlet, Oshawott & Cyndaquil ARE Starter Pokemon, but why I don't consider them to be starters in Legends Arceus is due to how the player is transported back in time to the point where humans live in fear of Pokemon and Pokemon Trainers aren't a thing as of yet. You're introduced to Rowlet, Oshawott & Cyndaquil not as Starter Pokemon but rather as research subjects for Professor Laventon. Because Laventon didn't want the player to brave their Survey Corps exam single handedly, and that the Pokemon want to join your team, Laventon allows the Player to initially take one of them. Depending on how quickly you can fill out your Pokedex, Laventon will allow you to take one of the two Pokemon you didn't initially pick before allowing you to take in the final Pokemon. Legends Arceus doesn't use these Starter Pokemon as Starter Pokemon being they literally don't refer to them as Starters, but rather as a means to encourage you to fill out your Pokedex.

6. Literally Any Mystery Dungeon

In the Pokemon Mystery Dungeon series, this series is well known for how the game starts out with a questionnaire. This questionnaire's purpose is to evaluate your personality and match you with a Pokemon that fits your personality best. The Pokemon that you the Player can control includes both Starter Pokemon and Non-Starters such as Meowth, Riolu, Eevee, Vulpix, Skitty, Munchlax, Axew and many many others. While you CAN choose who your Partner in crime is, it DOESNT have to be a Starter Pokemon. You can literally choose whichever Pokemon to your hearts content as your Partner as long as it's not the same Typing as the Pokemon the game had already chosen the Player to be. Such as you won't be seeing a Charmander and Cyndaquil on the same team. Depending on which Mystery Dungeon you play, you're later given the opportunity to Evolve you or your partner OR you can completely abandon the player/Partner Pokemon for literally any other Pokemon that exists. Therefore, have fun! You have a wide selection of Pokemon to choose as your Partner Pokemon.

7. Pokemon Let's Go Pikachu & Let's Go Eevee

Pokemon Let's Go Pikachu & Let's Go Eevee are remakes of Pokemon Yellow. In Pokemon Yellow, the game takes a story more similar to Ash Ketchum within the Anime. Much like Ash, The Player isn't given the opportunity to pick out one of the traditional Kanto Starters: Charmander, Bulbasaur or Squirtle. Depending on which game you play, the Player is instead given no choice of their Starter at all. As expected, if you bought Let's Go Pikachu, your Starter is Pikachu. If you bought Let's Go Eevee, your Starter is Eevee. You also aren't allowed to evolve Pikachu and Eevee by the way, as Pikachu & Eevee refuse to evolve/guilt trip you into not evolving them, and players will box/stop using their first Partner not too long after obtaining them.

Which Non-Traditional Starter Pokemon is your favorite?