What if you have not been to court over child support and you sign over your rights, could the other parent still take you to court for support?

Yes. Unless the child is adopted by the other parent's spouse.

But read this (https://www.askmehelpdesk.com/family-law/signing-over-rights-read-first-116098.html).

The issue is that you can't "sign over your rights" not unless there is a partner for the custody parent to adopt. Rights can be taken away by CPS for various reasons, and at times in the US in some states there are a few reasons the custody parent can take rights away.

But in general it is a myth that you can sign over your rights.

Also normally if rights are taken away, except for adoption, child support is still owed anyway.

There is this myth that a parent can "sign over their rights". But its only a myth. So anything you sign that says you give up your rights would be ignored by a court if the other parent decided to go after support in court.