How do I manually display a popup with the widget?

How To
1

Is it possible to add the widget and made it appears when a user clicks on a phone contact link?

2

Yes it is possible,

<script>
    // open widget window
    LiveCaller.$emit('ui.widget.open');

    // close widget window
    LiveCaller.$emit('ui.widget.close');

    // toggle widget window
    LiveCaller.$emit('ui.widget.toggle');
 
    // change language after widget load
    LiveCaller.$emit('app.locale.update', 'ka');

    // Listen to the widget window open event
    LiveCaller.$on('ui.widget.open', () => {

    });

    // Listen to the widget window close event
    LiveCaller.$on('ui.widget.close', () => {

    });
</script>