C172R Pilot reported engine knocking after takeoff resulted in expeditious handling return to departure airport with a flat tire on landing.

Narrative

Approximately 20 seconds after departing RWY XX and at least at or around 500 AGL; the engine began to produce knocking noises; and I began immediate action by notifying ZZZ DEP TRACON of the situation. After being unable to notice anything quickly in a short period of time; I omitted checklists due to the low altitude and the possibility of the engine stopping power production. During the short analysis of the situation; I double checked if the mixture was accidentally leaned out; which it was not and was fully enriched; and if the fuel tanks were set improperly; which was also not the case. Fuel starvation was also not the issue; since the aircraft had departed with full fuel; and flight planning calculations had indicated that only 20 gallons would be necessary to complete the flight; with ample reserves. With this quick diagnostic; I was unable to determine what the issue was; and instead prioritized returning to the airport; while being low and slow. I turned back towards the airport; notifying ATC of the specifics of the issue instead of a broad 'We're having issues; STANDBY' statement. I safely landed with the only noticeable damage being a flat tire; possibly due to a hard flat landing because of how quickly the situation was advancing. Firefighters were dispatched; and arrived on scene shortly thereafter. Here are my takeaways from the situations:- I did not do my best at maintaining Vg; since I had some engine power without making it knock too much. Instead; I was more focused on getting to the airport and landing on RWY XY instead of completing a full downwind back to RWY XX. - I had 2-3 seconds of inaction due to being surprised and having no experience in real in-flight emergencies out of training. However; I did not settle into a state of panic and maintained positive control of the aircraft and handled the situation to the best of my ability and knowledge; given how unique and fast the situation was advancing. - I made sure I was clear and concise when speaking to ATC; and did not let panic create miscommunications or rather; a lack of communication.Suggestions to improve safety:- Flight schools should include a curriculum or lesson where a case-study takes place of a recent emergency where knowledge surrounding it is readily available. Students and experienced pilots alike can be benefitted by seeing how others react. This also serves to reiterate that pilot should never hesitate to declare an emergency and squawk 7700. The readiness of airport staff; ATC; and firefighters is paramount to successful outcomes.