The conditions for forming quasicrystals and their approximants are stringent, normally requiring multiple length scales to stabilize the quasicrystalline order. Here we report an unexpected finding that the approximants and motifs of dodecagonal quasicrystals can be spontaneously formed in the simplest system of identical hard disks, utilizing the unstable feature of the initial square packing subject to mechanical perturbations. Because there is only one length scale involved, this finding challenges existing theories of quasicrystals and their approximants. By applying the same approach to a system known to form a dodecagonal quasicrystal, we develop decent quasicrystalline order in a purely mechanical manner. With the aid of thermal treatment, we achieve a significantly better quasicrystalline order than that from the direct self-assembly of the liquid state within the same period of time. In sufficiently low temperatures where the self-assembly of a liquid is significantly hindered, our approach still promotes the formation of quasicrystals. Our study thus opens a venue for high-efficiency search and formation of quasicrystals, and may have broader implications for the design and synthesis of quasicrystalline materials.