Fe-based oxypnictide superconductors were successfully synthesized at lower reaction temperatures and with shorter reaction times made possible by starting with less stable compounds, which provide a larger driving force for reactions. Using ball-milled powders of intermediate compounds, phase-pure superconductors with T(c) above 50 K were synthesized at 1173 K in 20 min. This method is particularly advantageous for retaining F, a volatile dopant that enhances superconductivity. Bulk superconductivity and high upper critical fields up to 392 T in Sm(0.85)Nd(0.15)FeAsO(0.85)F(0.15) were demonstrated.