C-172 student pilot reported engine failure during initial climb. Returned to departure airport and landed safely.

Narrative

On Day 0; I was conducting my second solo flight at ZZZ to practice local practice area. Before departure; I did a complete pre-flight inspection along with my instructor checking the control surfaces; fuel quantity; oil levels; tires; and general condition of the aircraft. Everything was normal and in working order. Then I was cleared to taxi to Runway XX via taxiway 1. I completed the engine run-up and all pre-takeoff checks in the run up area. Oil pressure and temperature were in the green; magnetos checked and working properly; and the mixture was set to full rich.I taxied on to Runway XX; aligned on the centerline; and began my takeoff roll. The aircraft accelerated normally; and I rotated at 55 knots. Initially; the climb was normal and the aircraft was responding well. However; when the aircraft reached about 200 feet above ground level; there was a sudden loss of power. The aircraft wasn't climbing and I could not gain altitude. I quickly verified that the throttle was full forward; the mixture was full rich; and both magnetos were on; but nothing improved the situation.Realizing I did not have enough altitude to continue climbing safely and no safe landing spot ahead of me I made the decision to turn back to the runway. I executed a 180-degree turn to line up with Runway XY I also let the ATC know about the situation trying to manage airspeed and altitude carefully while keeping the aircraft under control.I touched down at the intersection of Runway XY and Taxiway 2. The landing caused the aircraft to bounce slightly; and it continued rolling until coming to a stop near the end of Runway XZ. During the landing; the left main tire went flat due to the bounce. Throughout the incident; I focused on maintaining control and avoiding obstacles; and I was able to stop the aircraft safely. The aircraft was towed to the ramp by the maintenance. There was no damage to the airframe; power plant and the occupant.