The information in this article can help you when the game does not proceed past the initial loading screen in Splatoon 3, and appears to be stuck on a black screen.
What to do
Enable Airplane Mode on your Nintendo Switch console. If you are using a LAN connection, disconnect from that as well.
From the HOME Menu, start Splatoon 3. If this is your first time starting the software, set your player appearance, complete the tutorial, and then proceed to Splatsville.
Once in Splatsville, turn off Airplane Mode. If you were using a LAN connection, reconnect to it.
Press the X Button to open the menu, then select Lobby. You may be prompted to transfer your Splatoon 2 save data, and select a Splatfest Region.