You would really need 4+ years of college or a history of casting to get Riot's attention. I think at the moment Riot has like 15-20 Casters at the moment so I think they are fine in the casting department but I'm sure if you can make a name for yourself they can make room for you.
If you have passion to becoming a shoutcaster for Riot I would start a Youtube channel and cast some LCS games with Play by Play and give your 2 cents on how blue side can win the game or red side vice versa.
You will also build a rep for yourself and get your foot in the door.
Some casters played in the pro scene like Deficio,Jatt and Kobbe. Ninjas-Dignitas-CLG.
Some casters are more around the humor side of League to make things less stale like Phreak.
Others are more for their play by play side of things like Rivington.
Pick a game to cast about I would recommend Team Curse vs Complexity back in 2014. I'm recommending that game because it's about 75 mins long and it's good practice for you. Being it's a long game you will need to keep your "fans/audience" entertained for the full game while keeping up with your play by play for the full game.
Anyone can cast a game that is only 20 min long but can you do it for a game that is over a hour long ?
Work on your play by play casting, this should be the easiest for you if you already have an "encyclopedic knowledge" of champions and their abilities. Similar to Rivington.
Work on your pick ban part of the game. After a ban is made pause the game and talk about why X team banned that champion and same thing with certain champions picked for a certain team. This will help you with an idea for what the specific team will be going for. For example if blue team picks Jax that is a hint for you to talk about how blue team will be going for a more split pushing strategy etc.
Similar to Deficio.
While a game is in a stalemate situation you can talk about how each team can win based of different situations and strategies. Similar to Jatt.
Last but not least be funny and give a fresh outlook on things. Sure you can cast but if it's cut and dry people will get bored so pull a few jokes once in a while but make it League related last thing you want is to pull a "race" joke or a mama joke. Make it League related or not offensive and you should be fine. Similar to Phreak.
Start a Youtube channel, build followers, make a name for YOURSELF, and Good Luck. Laters