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Monolayer FeSe on SrTiO₃ has a greatly enhanced superconducting T_c compared with the bulk FeSe, but long-time annealing was required to achieve the superconductivity. We grow 1-unit-cell to 5-unit-cell thick FeSe films on SrTiO₃ and deposit small amounts of additional Fe onto the as-grown films. We find that adding Fe atoms induces superconductivity with high Tc without the anneal process, indicating that the as-grown FeSe films possess Fe vacancies. In the 5-unit-cell sample, we tune the reconstruction and stoichiometry by alternating deposition of Se and Fe and switch the FeSe multilayer between an Fe-vacancy phase and the superconducting phase. We offer an easy and time-saving treatment method compared to the many hours of annealing. This research unveils the essence of the anneal is to improve the stoichiometry, which is crucial for the properties of FeSe on SrTiO₃.