Air carrier First Officer reported ATC gave the crew vectors that were different from the company's charts for a visual approach which resulted in a EGPWS terrain warning and missed approach.

Narrative

When checking in with approach control; PM requested the company specific charted visual approach. We were vectored to charted visual approach in a mountain environment. PF saw the runway and was cleared for the approach in very comfortable position. After the clearance; approach gave us a new vector to join the course. The vector was very far from the vector we needed and it took us far from the approach and closer to the terrain. After PF completed the turn per the instructions it was clear that this would not work. PF immediately turned back to the original direction planning to correct and coordinate with approach. After the turn back PF started a shallow descent to the restricting altitude in that segment. Quite fast we got 'terrain' and 'pull up' warning. We executed the escape maneuver that cleared the enhanced ground proximity warning (EGPWS) immediately. PM called missed approach to ATC. The terrain was clearly visible and we were clear in the front but we believe that the terrain under us was close and caused the warning. At this point approach asked us the reason for the missed approach; and we told him it was for an EGPWS and requested vectors back to the approach and explained how he have to do it. He vectored us correctly and allowed us to do the approach as per our needs and we continued to landing with no additional problem. Cause: We failed to recognize early enough that the vector approach gave us was very wrong and failed to realize that it put us much closer to the terrain therefore not in a position to descend per the approach requirements for that segment.Solution: Recognize when ATC instructions conflict with surrounding terrain and charted approach procedures. Say unable" and request different instructions when something differs from the agreed upon procedure; especially where terrain is a factor. Be quick to request new instructions from ATC when you recognize that the current ones will not work."