Corporate Captain reported they inadvertently crossed a runway threshold without clearance resulting in ATC directing a go-around for landing traffic.

Narrative

During taxi from the ramp ZZZ ground XXX.XX gave us instructions to taxi from Taxiway 1 cross runway XXL and runway XXC continue [taxiway] 1 to [runway] XYL and to follow the commercial aircraft. After passing runway XXC we completed are 'taxi before takeoff checklist' and continued taxing on [taxiway] 1 up to [runway] XXL.At just before [taxiway] 2 instruction; I asked the First Officer to switch to ZZZ Tower frequency XXX.XX as soon as we switched frequencies; we heard tower 'line up and wait for a full-length Takeoff/Departure runway XYL. I queried with the First Officer and he confirmed that was the tower's instructions and I asked for the Runway Lineup checklist. As I started my taxi on [taxiway] 2 to runway XXL I immediately stopped due to aircraft approaching runway XXL; ZZZ Tower at the same time also instructed us to stop immediately and we had inadvertently partially crossed over XXL/[taxiway] 2 runway threshold. ZZZ Tower instructed the approaching aircraft for XXL to initiate a go around; after ZZZ tower cleared the landing traffic for the go around; instructed us to taxi on XXL make a right on 2 to 3 and had us call the tower to provide our information.Contributing factors - 1.'Not hearing the full tower instruction's as we made the switch from ground frequency to tower frequency but just the partial instructions from tower and hearing 'line up for a full length.' 2. Unfamiliarity with departing from runway XYL at night from ZZZ airport. 3. New crew pairing; first officer was not pressing the correct transmit button on the yoke when communicating with ZZZ Ground and Tower as he is use to flying from the left seat as PIC. Corrective Action - 1. Query Tower for full read back of instructions if only receiving a partial transmission and both pilots are unclear of the partial transmissions as we switched frequencies from ground to tower frequency. Human Performance considerations - commuting in via the airlines from ZZZ1 to ZZZ and passengers running behind schedule may have been factor being close to the minimum rest for the next day.