A Grumman Tiger pilot reported they taxied on to the runway after Tower cleared them for takeoff. A B737 was on short final and initiated a go-around.

Narrative

I requested to taxi from the FBO to the active runway XX at ZZZ with the ground controller. He authorized me to taxi and asked if I would want an intersection departure at taxiway 1. I declined the intersection departure due to high density altitude and proceeded to the run up area of runway XX. After reaching the run up area and after completing preflight checks; I switched to tower frequency. I heard the controller talking with a Vision jet inbound at 20 miles. I believe that the Tower controller and ground controller were the same individual based on his voice. I asked for clearance to take off on runway XX and was told that I was cleared for takeoff runway XX. I believe that I checked final and saw nothing but there was thick smoke in the area due to numerous forest fires. I taxied onto the centerline of the runway when I heard the tower controller clear an air carrier flight to land on runway XX. The pilot of the air carrier flight said that 'that wasn't going to work' and stated that they would be going around. I glanced back and saw an air carrier 737 on short final beginning to go around and I immediately exited the runway back to the run up area. The tower controller acknowledged the air carrier go around and when I notified the controller to notify him that I had exited the runway he didn't immediately acknowledge. When I informed the tower controller that I was ready for departure I was acknowledged and subsequently cleared for takeoff; again; on runway XX.I taxied onto runway XX centerline where I did a full throttle leaning (approximately 20seconds) and then departed runway XX. I was cautioned about wake turbulence from the recent go around air carrier 737 and asked to offset south of the centerline to allow another air carrier flight to depart; which I did. It seems to me that there were several contributing factors that resulted in a near miss / runway incursion event (albeit as directed by ATC). 1) The controller was task saturated with manning both ground and tower frequencies. 2) Heavy smoke/haze in bright light may have diminished the controllers and my assessment that final was clear. 3) The first contact for the Tower Controller with the air carrier flight was when he checked in and was cleared to land. Perhaps a late hand off by Approach. Fortunately appropriate action on the part of the air carrier flight crew and myself resulted in deconflicting a near miss avoiding an unfortunate outcome.