If I understand your question, you have a proxy server that blocks internet access until the end user has authenticated. By "blocks" I mean: If your proxy receives a request for https://google.com, it will spoof the requested host (google.com) and return a 302 redirect header to a login page that is hosted on the proxy itself. This a very common scheme that can be found in public wifi in McDondald's, Starbucks, etc. and is also pretty common in corporate settings.
The issue with this is of course the spoofing. Spoofing google.com will cause a cert error, although (until recently) the user could click through this. The introduction of HSTS now makes it impossible to get around the cert error and proceed to the proxy's login page, and there is little an end user can do to override it.
As an end user, I have been encountering this as an issue more and more lately. The way I have been dealing with it as an end user is to navigate to a site that doesn't have HSTS (e.g. CNN.com) or to navigate by IP (e.g. http://192.168.0.1). These will also get intercepted by the proxy but I can get around any cert errors.
I believe the "correct" way for a proxy server to demand authentication is not with a 302 redirect but with a HTTP 407 Status Code which means "proxy authentication required." The proxy should respond with this header instead of the 302 redirect. The browser should know how to interpret HTTP 407 and present an appropriate dialogue for collecting user name and password.
Second option....If this is a corporate network and you have the ability to push group policy, you could use it to set the browser home page to the proxy login page, thereby eliminating any need for redirections.