Air Carrier First Officer reported a fumes event during preflight. Maintenance was unable to detect any fumes in spite of the flight crew experiencing physiological symptoms. Captain refused the aircraft which resulted in an aircraft swap. .

Narrative

We were delayed waiting for our Aircraft X to arrive from a pressurization check flight at gate. I placed my bag on the jet bridge and put on my rain jacket and safety vest to perform the exterior preflight. Captain turned on the lights and pumps for me and started the cockpit checks. I performed the walk around in the rain and at a normal pace and didn't smell any fuel; fumes; or feel anything out of the ordinary. I arrived in the flight deck and Captain said he call Maintenance to investigate a fumes smell. I could smell something that smelt to me like exhaust fumes. The Mechanics came on board and I got up out of my seat because I started feeling dizzy and a headache. I started feeling better once off of the airplane. I then went into the cabin and it was worse in the center of the cabin. I asked the Flight Attendants to step off of the airplane and once they had fresh air; they started feeling dizziness and headaches. I realized that one of the Flight Attendants had stayed on board and went back to get her off of the airplane. She was oblivious that we had left the aircraft and said she started feeling dizzy once she started walking off of the airplane; but was better once off.When the caterers opened the cabin doors it started getting better and less smell was noted. I walked the cabin after the caterers had left and if was better but I still felt dizzy and a rush of clarity once I got off the airplane. I was hoping the Mechanics would have some symptoms but they all said they couldn't smell anything of felt any different. I asked the Lead Mechanic if he had a Carbon Monoxide CO detector; and he scoffed at me. He said that would be a process and that there were fumes everywhere on the ramp and it wouldn't do any good. I didn't say anything; but when I was working as an A&P we had small CO detectors around our shoppe.I voiced my concerns to Captain that I didn't feel safe on the aircraft because I was getting dizzy and was getting headaches; so was the crew; and it wouldn't be safe for the passengers. Once off of the airplane I was starting to feel normal again.Captain refused the aircraft and we eventually got a different airplane with no issues and we conducted a safe flight. The crew was well and fit for flight once we were away from whatever was making us Ill on the last airplane.