The pilot reported that the airplane encountered a crosswind gust just as it lifted off during takeoff, which caused the airplane to drift toward the south side of the runway. The pilot described the encounter as uncontrollable; full aileron and rudder inputs were unable to maintain control. The airplane subsequently impacted the ground and came to rest inverted about 50 feet from the initial impact point. The pilot did not report any failures or malfunctions associated with the airplane before the accident.