Tickets are off until an admin turns them on. The switch is in the header of the Tickets page itself, not on a Settings page, so that is where to look.
Flip the switch
Open the Tickets page from the Customer Service sidebar.
In the header, use the Tickets enabled / Tickets disabled switch.
Only a Super Admin or Admin can flip it. A member with ticket access sees the switch greyed with an "Admins only" note.
What turning it on does
The Tickets entry moves up to the main sidebar, and the New ticket button and the board appear.
A convert to ticket action appears on chats in the inbox.
A demo ticket is added so the board is not empty.
It also changes Users Capture
Turning tickets on sets Users Capture to Mandatory and starts collecting every customer's email, so you can still reach people after a channel's reply window closes. You will see: "Tickets activated. Email is now collected from every customer." This does not undo itself: turning tickets back off leaves Users Capture on Mandatory, so change it back by hand if you need to. See Configure Users Capture.