Genshin Impact, like all games, is prone to some error messages. They will pop up in different circumstances and will mean different things. Some are easy to fix, while others render you powerless until the developers resolve issues with the servers.
If you have been hit with the “Not Init” error message while trying to log in, then it’s good news, as this one is easy enough to fix. All you should need to do is restart your game, and that will resolve the issue, allowing you to log on. This error message will normally pop up when your game needs to download some new information. This is not the full updates that add new content, but just the small downloads that occur every time you turn on the game.
If that download is interrupted for any reason, you will get the “Not Init” error when trying to connect afterward. You should notice the screen is slightly different afterward, with fewer options, and pressing X to log in will fail.
Restarting the game will give it another chance to download the information that it needs, and everything should be fine afterward. If that doesn’t work, powering off and back on the console should resolve the problem for you.