B737-800 F/O reported returning to the departure airport after experiencing strong fumes in the cabin.

Narrative

This was the first flight on the aircraft after an engine change. During engine start there was a strong exhaust smell which is not unusual given the strong gusting crosswind. During initial climb I sensed that the pack was blowing hot (it is not unusual for a large temperature swing after the airflow increases with takeoff thrust); and made an adjustment to the cabin temp knobs. Immediately after chiming out of sterile at 10;000 AGL the FAs called the flight deck. As pilot monitoring I answered and was informed of a strong smell in the back of the aircraft. The FAs relayed that the odor smelled like burning wires or cables. I requested with ATC to stop the climb at 16;000 MSL. Captain transferred the aircraft to me; contacted the cabin crew for more information and made the decision to return to ZZZ. I requested priority handling; was cleared to ZZZ via direct and began to prepare for the approach. The Captain ran the checklist while the crew relayed that the smell began during the takeoff roll and dissipated while they were speaking to us. They also informed the Captain that two FAs felt ill. We requested Runway XXR; ARFF (Airport Rescue and Firefighting); and paramedics to meet us at the gate. The return was uneventful. We were put on vectors for the visual XXR; performed a normal landing and exited the runway at Taxiway 1; to hold short of Taxiway 2. ARFF did a 360 inspection and followed us to the gate. ARFF boarded the aircraft and did a walkthrough as well as examined anyone who was feeling ill. Captain debriefed the event; completed the required paperwork and provided detail to maintenance personnel. I moved on to prepare the replacement aircraft.Cause: Event was handled well by all crew members. Captain made his decision quickly and affirmatively. An earlier notification (prior to exiting sterile) would have been appropriate in this situation.