The defect-free neutral atom array has emerged as an ideal platform to investigate complex many-body physics of interacting quantum particles, offering the opportunities for quantum simulation and quantum-enhanced metrology. To fast build a large-scale quantum system, we design a sorting-atom algorithm with maximum parallelisms. Compared with previous protocols, our method saves the rearrangement time by sorting row-by-row and is also universal to arbitrary periodic patterns with no need to change the hardware. We present the generation of a defect-free square and other periodic geometries and demonstrate the potential to scale up a defect-free array to 2500 atoms with only about 180 steps of rearrangement.