Air carrier First Officer reported an airborne conflict during approach to SGU non-towered airport that resulted in a TCAS RA event and go-around. Reporter suggested the traffic volume at the airport was sufficiently high that a control tower would enhance safety.

Narrative

On the RNAV 19 approach in to SGU; Center ATC informed us that there were no known or observed traffic in the vicinity and to change to Advisory frequency. I was making multiple position reports as PM. As we were approaching SGU we noted a target on TCAS 3000 ft. low 12 o'clock opposite direction and climbing as we were descending. Once we got closer to the target we made visual contact. At this point the target was about 10 - 11 o'clock; still opposite direction but it appeared that we would pass by and be clear. We still had visual contact when we received a traffic alert but decided to continue given the path of both aircraft and visual contact. Once the target reached our 9 - 10 o'clock position the CA and I both lost visual contact - this is when we received the RA. Since we no longer had visual we complied with the RA. At this point we were well above glidepath after the final approach fix and elected to perform a go-around. We switched back over to LA Center and informed them of what had happened; they responded that they still weren't showing any traffic in that area and weren't talking to anyone in that area. Not once did we ever hear the traffic make a radio call. We came back around and made a successful approach and landing. After landing we had multiple passengers tell us they saw the small plane and that they couldn't believe how close it had turned to us or how close it got to our plane.The cause of this event was 1. the target aircraft was not communicating on the CTAF frequency nor with ATC. 2. Our crew lost visual contact with the target as it went below and to the side of us into a blind spot. 3. ATC did not show and was not aware of any traffic in the area. 4. After we complied with the RA we were well above glidepath and after the FAF.It will greatly improve safety to have a Control Tower in place at this airport as the number of GA aircraft has increased tremendously. I also believe that speaking to the Airport Management developing a letter of agreement with airport tenants and hangar owners as to the entry and exit of the airspace as well as departing straight north on the approach path to 19.