Offline Support

If my game is playable offline, would it be possible for the player without an internet connection to create and save the avatar locally?

If yes, please direct me something how to do it

Hello and welcome to the forum!
if you are loading avatars in the engine with the avatar loader and not at runtime, when you build the game, it will work also offline. If you want players to load their avatars, then they would need to have an internet connection, at least the first time loading the avatar, then you can use Avatar Caching. If avatar caching is enabled, every time an avatar is loaded, its assets are stored locally. This is usually enabled by default for optimization. You can find more information about it in our documentation here: Avatar Caching | Ready Player Me