Quick answer
[Official] Big Walk saves group progress automatically on the host's game. The host is the keeper of the save, must start each returning session first, and must host again when the group wants to continue from the same point.
Plan the host before starting
- Choose a host who is likely to attend future sessions.
- Have that player start the session and load into the world before guests connect.
- Let guests join through the active friend-games list or current Join Code.
- For the next session, have the same host load the saved journey before the group joins.
What happens when the host leaves
[Official] When the host stops the session, every guest is disconnected. Another player can host a session, but the reviewed official guidance does not say that doing so transfers or continues the original host's save.