If you want to open the live chat from a button or link of yours on your website you can easily achieve it with the onclick html tag.
If you have a <button> or <a> element to open the live chat when someone clicks on it just add the onclick="customerly('open')" to it.
<button onclick="customerly.open()">Click me</button>
Or if you are using an <a> element follow the example below:
<a onclick="customerly.open()"> Link to click </a>