Are you wanting to make sure that a new conversation starts after the period in time?

You may want to create a workflow specifically for when you start an outbound message via chat, that ends with closing the conversation in workflow after you’ve snoozed it for X amount of time.  

Hope this helps. 

Thank you for your response. The use case I have is that when I turn off chat  (for example for a holiday), we disable the option to let the user start a chat and we do have a setting on to prevent visitors from replying to a closed conversation. However, we’ve noticed that the users can still respond to an existing outbound chat that they might have previously received so I’m trying to figure out if there is a way to prevent replies to outbound chats that are no longer active. Is that possible? Thank you!