B747 First Officer reported engine damage during engine start resulted from FOD in the push back area. The aircraft was towed back to the gate for maintenance action.

Narrative

We arrived at Aircraft X for a flight on time; if not a bit early. I performed the walk-around upon arrival. I did not see anything out of place with the aircraft other than I observed the fueling door on the left wing open and the aircraft being fueled from the right wing. I also observed the agent fueling the aircraft walk over and see that the left fuel door was open. I checked after fueling to see if the left fuel door had been shut and it was. We blocked out from ZZZ at XA:24z; a bit late due to loading. I was on the observer seat; the other First Officer was the PF (Pilot Flying) and the Captain was PM (Pilot Monitoring). We began the push back off of I believe stand XXX on the Ramp a few minutes after blocking out. Shortly after the push back began; about half the distance of the stand length; we received clearance to start the engines from the Pushback Crew. We started engines 1 and 4. Engines 1 and 4 started with no abnormal indications on the flight deck. After engine 1 and 4 was running; the aircraft was now in the alley facing East. We started engine 2 and 3 with no abnormal indications on the flight deck. After what we believed were 4 good engine starts; and asked for the disconnect and the Pushback Crew Member on the headset asked how engine #4 was running. After reviewing the engine page; #4 appeared to be running ok with the only exception being that the ITT was about 8 degrees or 10 degrees above the other engine's ITT. The Pushback Crew member said that someone on the ramp witnessed sparks that had come from engine #4 and told us to stand by. He then told us that they wanted to tug the aircraft back to the stand and shut down all engines and prepare for being towed to the stand. We returned to the stand and secured the aircraft. The stairs were brought to the aircraft and we exited the aircraft. Maintenance had engine #4 cowling open inspecting it. Damage to the cowling inlet and fan blades was visible. The rest of the crew and I waited on the ramp and were shown the damage to the engine and the metal found outside and inside the engine by Maintenance and other Ground Personnel. An individual brought over pieces of metal that they said they found in the engine; and another individual had brought over a bolt about the size of a pen and another piece of flat metal they said they found in the alley where the aircraft had been pushed into. We then returned to the hotel and entered rest.