A319 First Officer reported receiving an ENG 1 STALL ECAM message that was then accompanied by a surging engine noise. The flight crew performed an inflight shutdown of Engine #1 and proceeded to divert.

Narrative

While starting our arrival into ZZZ we were issued a descent. The Captain left to take a lav break. As soon as they left the flight deck a brief ENG 1 STALL ECAM message was received and that was accompanied by a surging engine noise. The message quickly went away. When the Captain returned; I informed them of the issue. Soon afterwards; we noticed that the #1 Engine EGT was rising rapidly. It fluctuated multiple times until it remained in the red arc with increasing temperatures. We received another ECAM due to that issue. The Captain delegated pilot flying and the radio duties to me while they completed the ECAM procedures. I briefly recall that we received multiple ECAMs that seemed unrelated to the event after our exchange of duties. Those ECAMs seemed to disappear after awhile. The #1 Engine was shut down inflight due to the damage.I was focused on flying the aircraft and communicating with ATC during this very busy period of the flight. We elected to divert to ZZZ1 as we were abeam the airfield while at altitude. As we were being vectored towards the airfield; the ECAMs; checklists; briefings; and communications with all necessary parties were completed before exchanging the controls to the Captain to begin the ILS XX approach into ZZZ1. We were met by firetrucks after landing; and they performed an exterior inspection and determined that the aircraft looked okay and that the inspection was satisfactory. We proceeded to the gate and deplaned all the passengers and contacted Maintenance.