I'm trying to serve my cloud storage content using custom domain over https. Currently, I'm using Amazon S3 with CloudFront to deliver the content using custom domain over https. But S3 with CloudFront is costly, So I'm now searching for an alternative.
At the moment, google cloud storage only support HTTP. As per documentation To serve your content through a custom domain over SSL, set up a load balancer, use a third-party Content Delivery Network with Cloud Storage, or serve your static website content from Firebase Hosting instead of Cloud Storage.
I was able to find this blog which might help you on the setup.
With that being said, if you are looking for functionality like this you may also try with App Engine, as by default, HTTPS connections on your custom domain will automatically be enabled using managed SSL certificates. You can visit this link for more details. Also, there is a there is a feature request submitted to support auto managed SSL with GCLB.