The US Army has some information on this process for service members stationed in Germany who want to get a EU digital COVID Vax certificate. According to this, the steps are as follows:
Locate a pharmacy ("Apotheke" in Germany"). Not all pharmacies offer the digital certificates. The website https://www.mein-apothekenmanager.de/ allows you to find ones that offer this service specifically (in Germany). Under "Serviceleistungen" select "Digitales Impfzertifikat".
Take your CDC card to this pharmacy. You will also need to present a valid photo ID, best chances of success would probably be a passport.