C172 Flight Instructor reported while observing student's first solo the student lost control of the aircraft during landing resulting in a prop strike.

Narrative

My student and I were at ZZZ going to do his first solo as that is the only approved airport other than ZZZ1 and ZZZ1 seemed very busy. We did 3 landings together. Two normal and one power off; along with two go-arounds due to traffic conflicts coming in on runway XX for an approach. The first A/C was not making radio calls and was on short final for runway XX while we were on short final for runway XY. I instructed on how to perform a go-around by sidestepping to the right to avoid traffic. He did so and executed a textbook go-around. The second one involved a helicopter. They reporteded they were on a checkride; so we went around and sidestepped to the right again. My student showed me a good landing afterwards and we decided that he was ready for solo. Winds at the time were reported to be 230 at 8 knots. These conditions were consistent with what my student handled before and he was landing great today in these same conditions. Prior to releasing him I made another visual check of the windsock that was hanging limp. I signed my student's endorsement and sent him on his way for his three laps. First landing ended in a textbook go-around due to feeling unstable. Second and third attempt were very good. My student waited on the runway after the 3rd approach to let a helicopter land and taxi off the runway. Afterwards he took off. As he was in the base a twin engine airplane was coming in and declared incorrectly over the radio that he had priority because he was faster. Inspite of being lower my student went around and sidestepped to the right just as we did earlier to avoid a traffic conflict. On his next lap; my student was coming in on a stable approach until I felt a gust of wind behind my back as I was watching him. He was just about over the threshold at this point. I heard him add some power to make the runway and it appeared that he was in a good flare attitude and would make a good landing. He touched down gently just as a second gust of wind caused him to balloon. I heard the engine increase as my student attempted a go-around just as a stronger gust caused him to weathervane. The aircraft touched down again only this time in a crab to the right. The right main came off the ground resulting in the the prop striking the runway. The airplane did not look like it had any other damage. I thought he initially saved it and was going to taxi back from my perspective until I realized that the prop had stopped. From this point I realized that he may need help; I saw him get out of the airplane and He looked to be safe. I could not see any damage until coming closer to the airplane. I contacted dispatch and notified the ACP (Assistant Chief Pilot) on duty after I sent a message to my student to stay put and I will try to be their shortly. I then talked to my student for a bit until airport management was able to come out with two trucks to head to the disabled aircraft.During the entire time we were at ZZZ; the windsock; onboard wind indications and lack of choppy rides were consistent with the favorable first solo conditions as reported by the ASOS. The winds were not forecasted anywhere to become gusty and it wasn't until the new metar that came out that said it was gusting up to 19. This updated after the accident. There were no TAF's in the surrounding area that was reporting this and conditions were good up until that point. My student did a great job of shutting down the aircraft and going through the emergency procedures by memory and remained calm throughout the event. After the accident I took pictures of what had happened. There only appeared to be prop damage and no damage to the firewall. There was also no evidence or debris on the runway from where the prop struck. We then were able to tow the aircraft to a spot utilizing the airport's tug and tied it down afterwards. We had previously trained in crosswind conditions over the past few weeks practicing landings and my student was exceeding my expectations after some practice. We had practiced on a very windy day as well and he was able to understand his limitations; but with me in the cockpit to assist as necessary. We trained on Day 0; Day 6; Day 7; Day 8; Day 9; and Day 14. My student had a small break as he was up for his stage check between Day 14 and Day 23. On Day 23 he had his stage check and the stage check instructor said he did very well. When we flew today prior to the occurrence my student was doing very well and demonstrated good aeronautical decision making throughout the flight.