Hi, yes you can by dragging the website's favicon onto your desktop or onto the Dock in the far right near the Trash which is the User area. Clicking the favicon will launch Safari or your web browser of choice & open the website directly.
If you click in the URL bar you will see the favicon to the far left as in my attached pic. The favicon for Mac Help is a blue apple. Just drag it off the URL bar onto your desktop.
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