Air carrier First Officer reported receiving a GPWS alert during takeoff from OAJ airport. The First Officer stated they were not sure what triggered the warning as they were reportedly clear of terrain.

Narrative

On departure OAJ to ZZZ we were given takeoff clearance from Tower - cleared to takeoff Runway 5 left turn heading 290 - with an altitude of 3000 feet.I was Pilot Flying and I was hand flying at the time. Conditions were VFR. I elected to start the turn at 1000'. As we were in the turn Tower was swapping us to Departure and the Captain (PM) was checking on. At 2;500' I started preparing to level off for 3000' at an airspeed of 200. I was over VFTO and flaps were up at that point. I was a few degrees away from rolling out on the heading. As I was preparing for that; the GPWS alerted us to Pull Up". It startled us both and neither of us understood why - we knew we should have been clear of terrain and the Captain visually scanned the area for anything we could have missed. I continued to climb; but I had already taken the thrust levers out of the climb detent. Meanwhile; the Captain is trying to keep up with ATC instructions but I continued the climb past 3000' to 3700'. ATC tried to give us an altitude and heading change but I was trying to focus on the GPWS; get comfortable and get the autopilot on so I could take the load off. The Captain informed ATC we had to comply with a GPWS warning. But while we were caught up with everything going on; it took me a few too many moments to realize my airspeed was bleeding off because the trust levers had been taken out of climb. I caught that airspeed had bled off to about 170kts and I added the power back in. The startle factor in the GPWS definitely got us. Between that and ATC we suddenly got very behind the airplane. I was trying to maintain control and the Captain was trying to communicate. Here's what we should have done differently: with the GPWS warning I should have added the power back in and climbed immediately and the PM should have told ATC about the GPWS. That led to fumbling with the FCP panel and a longer time to regain control and assess what had given us the warning.After getting things back to normal; we returned to Tower frequency on Comm2 and verified we had complied with their departure instructions. We had. Maintenance Control was notified when we arrived in ZZZ. Cause: Unsure what caused the GPWS; but the startle factor and the workload going on at the time led and trying to keep up with them led to the other deviations on altitude and airspeed."