Air carrier pilot reported receiving a RNAV departure clearance that placed the aircraft in a controlled flight towards terrain situation. Flight crew requested a turn away from the terrain and continued the fight with no further issues.

Narrative

The clearance we received from SBGL Clearance Delivery included the EVRAD 1A RNAV departure. According to our Company page; we can not accept that clearance. I explained that to the controller. He gave us a new clearance; after takeoff cleared present position direct EDNAM. I asked him to spell out the fix to make sure I heard correctly; then read back the clearance. After takeoff we headed directly to EDNAM. We were then switched to departure control. Upon contact we were asked; What's your condition?" We told her everything was okay. She then asked why we were not flying the EVRAD departure. We explained our clearance. She then started asking about climbing rate as we were approaching an area of high terrain. We had identified the area on the terrain display and increased our rate of climb. To be safe; we asked for a left hand turn to avoid the area. Once clear; we asked for direct EDNAM and continued. It was my first time to SBGL. The controllers in Brazil have very heavy accents.Company should work more closely with Brazilian Authorities to ensure we get proper clearances."