Test that can connect to a production database before deployment to production?

Not sure what this type of test is.

My team consistently deploys a new API server that's supposed to connect to a database, but only some of the times is that connection successful. We're trying to design a test that can catch that beforehand. However, I've never run a test that is essentially using prod credentials before actually going to prod. I've only ever tested in lower envs with lower env credentials. What exactly is this kind of test called?