Use custom domain for your Google Sites. This video tutorial will show you how to setup your custom url for your Google Sites. You will need to be using G Suite Apps for business or education in order to do this. Follow these 3 steps to quickly setup your own domain.

Create a CNAME
Publish and name your site in Google Sites
Map your domain address in your Google Apps Admin Panel.

CNAME Record Values: https://support.google.com/a/answer/112038