Flight Instructor with student reported initiating takeoff with an aircraft on short final approach requiring them to go-around to avoid the conflict.

Narrative

During a Stage Check at the ZZZ; Flight Instructor (IP) and student (SP) were holding short of the runway for a few minutes. There was a multi engine piston aircraft on base leg at 700 feet; when SP made a radio call and began to enter the runway. By the time IP was able to do anything the aircraft was already past the hold short line.IP then instructed the SP to perform a 'No delay' takeoff as there was still time to perform the takeoff without a hazard taking place. SP did not increase pace and by this point the Piper Seminole was on final leg. When SP started the takeoff roll the Seminole had to initiate a go around to avoid us on the runway. The seminole also performed a side step to the right. After takeoff and throughout the whole situation adequate separation between both aircraft was maintained and a collision between the two aircraft was not a possibility as both sets of pilots reacted accordingly to the situation. A causal factor that may have contributed to SP decision to takeoff may have been deadlines set by university for course completions; followed by stress and nerves from it being the first check taken with the school.