You can increase your inventory of Pokémon and plates in several ways at the Shop. You can purchase Boosters that let you acquire Pokémon figures and plates, or you can purchase designated plates directly. Another option is to do a Material Trade, where you can get Pokémon you like by trading the materials you collect when you purchase Boosters.
You can earn Gems to open Time Boosters and purchase items from the Shop, too. You'll have Gems delivered to your in-game inbox each day you play; plus, you can earn Gems and other items by clearing daily missions. Look for opportunities to earn Gems as you play through the game and in League matches, too. Gems can also be purchased with real money for use in the in-game Shop.