In a written statement, the student pilot reported that the purpose of the flight was for him to complete his first solo cross-country flight as a step toward obtaining his private pilot certificate. The airplane touched down normally at the first airport on his three-leg flight. While on the landing roll, the airplane encountered a strong gust of wind, resulting in it veering to the left. Despite the pilot's control inputs, the airplane continued to the left and departed the runway surface, impacting a dirt berm adjacent to the runway. The nose wheel landing gear subsequently collapsed, resulting in damage to the engine firewall and right wing tip. The student pilot further stated that an airport traffic controller reported a wind velocity of 3 knots, gusting to 15 knots just prior to his attempted landing. The operator reported no preimpact mechanical malfunctions or failures with the airframe or engine.