1) Browser asks the proxy for new.site.example.com. 2) Proxy replies 404 (or some other error). 3) Broser shows you the error. 4) You ssh to the proxy machine.

1) Browser asks the proxy for new.site.example.com. 2) Proxy replies 404 (or some other error). 3) Broser shows you the error. 4) You ssh to the proxy machine. 5) Open the whitelist in an editor. 6) Add the site to the list. 7) Save. 8) Reload page in broser. Site partly works. 9) Repeat 6, 7, 8 for each CDN the site uses. 10) Eventually the site works properly.