If you can't sleep, then get up and do something instead of lying there worrying. It's the worry that gets you, not the lack of sleep.

Set the time after which the current quote is refreshed. Use a tool like Plash (MacOS) to set this page to your desktop's background. Tap the image to toggle unnecessary interface elements.

To load the site with the interface not showing, and with a certain refresh rate, set querystring parameters like so: https://andiquote.org/?showInterface=0&refreshDuration=300.