We present a computational method for polymer growth called "threading subunits for polymers (TSP)" that can efficiently sample solid polymer electrolyte structures with extended conformations. The TSP method involves equilibrating subunit (e.g., monomer) conformations that form favorable solvation ion shells, followed by consecutively connecting the subunits and minimizing the structures. The TSP method can sample polymers with good solvent-like conformations and from near-equilibrium structures in which ions are well-dispersed, avoiding unusual ion clustering under ambient conditions. Using the TSP method, the equilibration time can be reduced significantly by effectively sampling the polymer conformations near equilibrium. We anticipate that the TSP method can be applied to simulate various polymer electrolytes.