If you use Namecheap to host your domains, the steps needed to add a custom domain in TIME Sites vary a little from what you would do on most enterprise registrars. But no need to fear, as long as you follow these steps:
In website settings, make sure to enter in your custom domain without www at the front, e.g. https://example.com
Publish your website
Reach out to TIME Sites Customer Success (either your rep via email or on the support chat) to let them know you want to add a custom domain. Once you give them your domain (example.com), they will give you two values to create a new CNAME record in Namecheap. This CNAME is to create the SSL certificate for your site, NOT to point the site to TIME Sites.
Once you've added that CNAME, let your TIME Sites contact know, and they will provide you with a Cloudfront url to point your domain to TIME Sites. This requires you to make two additional DNS entries in Namecheap:
Create an Alias record with the following:NAME: @
VALUE: [your unique cloudfront url]
Create a CNAME with the following:
NAME: www
VALUE: [your unique cloudfront url]
And with that, your site is live and secure on TIME Sites!