Flight Instructor on training flight with student reported a runway incursion and a near miss with a glider landing at a non-towered airport.

Narrative

I was in C172 at ZZZ; I'm instructing from Right Seat; Commercial pilot was pilot flying and at controls in left seat. There were glider operations in effect at the airport. We are holding short of [Runway] XXR at [Taxiway] 1; Pilot flying in left seat made our calls on CTAF that we are taxing to hold short for landing traffic. We were listening to CTAF; had ADSB in; and visually cleared downwind Base and Final before taxing up to the hold short line for XXR We both only saw a 182 coming in high to drop the tow rope; and land long towards the end of the runway. There were people that ran on the runway to drag the rope out of the way; we were waiting for the people to clear of the runway with the rope and the 182 to clear the runway. We couldn't see the end of the runway due to snow piles at our end; so we announced we would line up and wait for the traffic to clear. The pilot flying announced our intentions; looked into final to assure there was no traffic on final and began our taxi once he verified there was no traffic on final. We heard some noises on the radio but couldn't understand it. He made a second call 'say again' someone replied 'don't takeoff; they're landing' I hopped on the brakes at this point we were on top of the hold short line. We both look at each other confused; about 15 seconds later an orange glider comes into view and lands about 15 feet ahead of us. We heard no radio calls from that aircraft; the tow plane dropping them; or the ground crew. The pilot flying visually cleared final approach and didn't anything; there should be more training and awareness for glider operations. I believe the reason we didn't see the glider is because they made a short base leg which we didn't see; and they didn't make one radio call in the pattern. We only saw and heard the 182 which already landed. I think there should be more training for glider operations; and more awareness.