If you have the Supervisor role,  you can delete tickets directly from the incoming list.

This action is useful if it concerns tickets that cannot be closed normally or should be withdrawn from the agents immediately. It is not part of the usual ticket workflow.

Open the ticket and select the "Delete" action:

This marks the ticket as “deleted” and can therefore no longer be found in the lists or in the archive!

Note that this may cause you to transfer ownership of the ticket. You should only delete obsolete tickets from the inbox if the owner is not logged in or cannot be reached.