Add the opening class
The supplied frontend recognises elements with the CSS class floaty-open. Add that class to an appropriate button or link using your theme or page builder's CSS-class setting.
For example, a page button labelled Contact us can open the same configured channel list. Enter floaty-open as a class name; do not add the leading dot used in CSS selectors.
Keep a usable alternative
The widget still needs to be rendered on that page. Its configured page, device, login and schedule rules apply; this class does not override those rules or create a second widget.
Test the trigger after saving and clearing caches. Use a meaningful accessible label, check keyboard activation and avoid links whose destination would confuse visitors if the widget is unavailable. Keep a normal contact page available for visitors whose browser does not run the frontend JavaScript.
This integration uses the supplied plugin behaviour. Custom page-builder scripts, altered themes and other click handlers can affect it and need testing on your site.