Hello Tiledesk Widget example page.
In this example the widget starts hidden and opens fullscreen.
        window.tiledeskSettings= 
        {
            projectid: "61f4fc7b9dabc200196914d8",
            startHidden: true
            fullscreenMode: true
        };
    
Use the buttons to show/hide the widget.
      function openWidget() {
        window.Tiledesk('show');
        window.Tiledesk('open');
      }
      
      function closeWidget() {
        window.Tiledesk('close');
        window.Tiledesk('hide');
      }    
    
Subscribe to onClose tiledesk event to manage up right close icon.
      window.Tiledesk('onClose', function(event_data) {
           window.Tiledesk('hide')
      });