Cloudflare worker as reverse proxy for webflow

hi

I am working on a project where we have a webflow project and the requirement is that different customers can point their own domain to a subsite with us.

Example:
career.customer1.com points to xyproject.webflow.io/page1
and career page of customer 2 points to xyproject.webflow.io/page2
and so on…

The goal is also that the url of the customer remains visible in the address bar and not the target url of Webflow Hence the reverse proxy

As the domains are managed by our customers, I cannot set up the domain in Cloudflare. However, I was able to make a CNAME entry at customer1 for a test, which points to my worker. However, when I call up the page, I get the error message 1001.

I.e. the subdomain ends up at Cloudflare, but I think the worker is not called (there is nothing in the logs)

Is it even possible to solve the problem in this way?

Many thanks