Light Transport aircraft First Officer reported they entered a runway while another aircraft was on final to the same runway. The other aircraft executed a go-around.

Narrative

We were at Thermal/Cochran airport in California (TRM) and were on our way to ZZZ airport. We had previously gotten a clearance on the ramp with a 'hold for release'. We taxied down to the end of Runway 35 and pulled off into the run-up area and I called SoCal to get our release. I tried a couple different frequencies with no luck; so I called the phone number on my phone. The release was given and I told my co-pilot we were good to go. He responded and said there was one airplane midfield left downwind; but hadn't heard anybody else. It had been really busy with activity that morning and leading up to our departure; so it was a little unusual. As we approached the runway about 30 seconds after receiving our release I checked final; and didn't see anyone and told my co-pilot 'clear right.' I called that we were entering the runway as my co-pilot started to taxi past the hold short line and heard someone call that they were turning final (the first call I had heard on the radio since my phone call) and I looked to see where they were. Knowing a lot of jet traffic I was expecting to see a jet on a 3ish mile final. I didn't see anyone but then saw someone offset of the final about 30° turning about a half-mile or closer final; almost in the middle of his base to final turn. He went around and the flight departed without further incident.Suggestions: I can only assume the other pilots action; but it seems that he decided to do a short approach; almost like a power-off 180 approach. It was frustrating for us as a crew that so few calls had been made by this other pilot; especially when (to us) it was an outside of normal maneuver. We could have; and should have been a little more vigilant. I should be looking for traffic on final AND on both bases at a non-towered airfield. As a crew we could have slowed down; and although we were paying attention; we could have been more focused on situational awareness. A control tower would also have avoided this situation.