A student pilot reported an NMAC occurred when they took off from a non-towered airport when an arriving aircraft which was on short final initiated a go-around.

Narrative

During taxi to RW XX for VFR departure at ZZZ we observed a man standing just off the runway videotaping a plane; presumably an instructor videotaping a student doing a solo; although there we no other aircraft on ADS-B in the vicinity. At the hold short of RW XX we observed the plane on ADS-B departing to the south (no factor). Then an aircraft (not on ADS-B) called left base RW XX while we were about to call for takeoff. My CFI says to takeoff before him; and I double check that he really thinks we should take off now and he says yes. I quickly enter the runway and immediately go full power. Around then; we hear an aircraft going around but the CFI assures me it is not the aircraft behind us. A few seconds later; we see a shadow go down the runway; confirming it was in fact the aircraft behind us going around due to us entering the runway right in front of them. I decide to do a shallow climb as to not climb into the other aircraft as my CFI looks for it above us. The other aircraft then reports turning crosswind and I continue the climb straight out.This was the first cross country of my commercial rating; so I feel like I should have taken authority and waited for the plane to land before entering the runway and taking off. My instructor seemed unfazed from the occurrence; but this reinforced my belief to wait before departing if an aircraft is on base or final; especially when flying a high wing aircraft that blocks the ability to see other aircraft landing on base or final. Furthermore; with the man standing on the runway videotaping; the non-ADS-B aircraft could have been a student and I'd like that to be the last time I rely on a (potential) student's Aeronautical Decision Making (ADM) to go around instead of causing an accident or worse.