Embed options for Google Sites
Google Sites allows you to embed Calendly using its native iframe gadget, which (depending on what site theme you're using) will look similar to this:
SETTING UP THE IFRAME GADGET
1. Open your Google Site and click the Edit button.
2. Select Insert > More gadgets.
3. Type "iframe" in the search bar, then select "Include gadget (iframe)" once that search result appears.
4. Add your Calendly URL to the "URL to content" box. You may also want to adjust the width and height, and remove the border and title (this is optional upon style preference).