Systems and methods for assembling a skin of a composite structure on an outer surface of an inner mold line layup mandrel. The systems and methods include receiving a plurality of ply kits, assembling the plurality of ply kits to form a skin segment that defines a portion of the skin, and affixing the skin segment to the outer surface of the layup mandrel. The assembling includes transferring a respective ply kit of the plurality of ply kits to a non-planar transfer tool, compacting the respective ply kit on the non-planar transfer tool, and repeating the transferring and the compacting for each ply kit in the plurality of ply kits to form the skin segment.