How can I help my girlfriend open up to intimacy through her depression?

Very difficult. Hopefully is getting medical help & treatrment for her depression. Lack of interest in intimacy is one the signs of depression. Perhaps you could accompany her on her dr's visit, and speak to dr. Otherwise try and be supportive. Try stroking, possible some shoulder massage. She will be very appreciative & loving once she is over the depression. Try to be patient. Good luck.
Better treatment. Depression frequently causes a loss of interest in normally pleasurable activities, including sex. The key here is for your girlfriend to work with her doctor to get complete, not partial treatment for her depression. This loss of interest is one of the signs of still being depressed. Most cases are thought related to serotonin imbalance in the brain and medications help, also exercise.