Unlocking characters in is not the most intuitive process, and there’s nothing that informs players how to get the material they need to do so.
It might be frustrating depending on how quickly you want to unlock the other playable characters. However, there is one way to get Abyss Stones, which is what you need to get the full roster of characters under your control.
While there are just three playable characters in right now, there will continue to be more characters added to the game for players to try out as the Early Access period continues. There are at least 6 more locked spots beyond Lapis and Goro that appear in the game, which means there are at least 6 more planned Breakers to play as.
Collecting more Abyss Stones will help you have what you need for the future as well. Abyss Stones are available specifically from the Crown Boss fights.
You must beat a Crown Boss in order to earn an Abyss Stone. While more ways to find them may pop up in the future, right now this is the only known method.