Serverless api behind cloudflare domain

I understand serverless doesn’t support custom domain names yet, but is there a way I could bring my api under my own domain with cors and cloudflare cname-s? Do you have any best practices how to land with a custom domain at the end?

What I’ve seen a couple of people do is have a Cloudfront distribution in front of APIG so you can do anything from custom domains to SSL easily and simply point from Cloudfront to your APIG. You can also set it up that only that specific cloudfront can talk to APIG through auth headers.