The element exist there. Probably UI of button is not appearing because of using delays or not rendering in given time but the element exist there.
Go to inspect and copy the unique identifier of “Start button” from normal browser(which is not running through automated script)
then use await page.click("button_Identifier");
and you will see start chat button has clicked and window moved to next step.
solved element is not visible on site using puppeteer [closed]