Hello,
In Cloud SQL you cannot get super privileges. However, since your end goal is to replicate from an external server, please review the relevant documentation in order to do this 1,2,3. If you require additional help in getting it accomplished, let’s say you run into errors while doing it, I would recommend you to contact GCP support as they would be able to work with you in getting the replication accomplished. Also, you could try posting any errors you may encounter in Stack Overflow and the community may be able to provide you with some insight since Google Groups is meant for conceptual discussions only versus Stack Overflow which would be a good place to post any error troubleshooting you may need assistance with.