At what point, if any, can a closed adoption through an adoption agency reveal the biological parents to the adopted child?

You may find this other post helpful. https://www.askmehelpdesk.com/adoption/how-do-find-birth-parents-names-closed-adoption-288417.html

At the point when a legal subpoena through the courts, who have been shown just cause to open the adoption, is served to the adoption agency.

In other words: You'd better have a reason a whole lot better than curiosity to open the records.

Generally, the only time closed adoptions are opened is because of a serious medical need.

Birthparents were promised anonymity at the time they chose adoption--and so were adoptive parents. Opening an adoption should happen because ALL parties involved are ready for that to happen. This is why I am in favor of using reunion websites, as it requires both adoptees and birthparents to register, which is their move toward wanting a reunion.

Yes about the only time is when there is a medical condition that is life threatening and finding blood family members may be the only hope.