The solo student pilot reported that, after completing three takeoffs and landings unassisted with his flight instructor, he took off for his first solo. He added that, during the first landing, the airplane "floated" in ground effect for about 4 to 5 seconds, and he added rudder to align the airplane with the runway centerline. He further added that the airplane's nose wheel was "not straight when it touched [down]" on the runway. Subsequently, the student pilot applied brake to maintain directional and then applied power to abort the landing, but the airplane veered off the runway to the right. He then reduced power to idle and stopped the airplane in the grass next the runway and awaited instructions from air traffic control. The left wing sustained substantial damage during the runway excursion. The student pilot reported that there were no preaccident mechanical malfunctions or failures with the airplane that would have precluded normal operation.