The sulfurization of co-evaporated Cu2ZnSnSe4 (CZTSe) thin films is studied. In this work, a relationship between the Na concentration and the further S incorporation in the CZTSe absorber layer is found. Na is added by a NaF precursor layer before CZTSe co-evaporation and/or by diffusion from the soda-lime glass substrate. Higher Na concentrations result in bigger grain sizes, higher S/(S + Se) atomic ratios and photovoltaic devices with higher V-OC, as investigated by SEM, GIXRD, Raman and I-V measurements. Results using an alternative substrate as ceramic verify the importance of the control of the Na content, which alters the carrier concentrations and elements distribution with much higher S and Na concentrations at the surface in this particular case. By using this methodology, it is possible to tune the kesterite band gap energy by the creation of S-gradient through the absorber thin film. This may provide a new approach for the control of Cu2ZnSn(S,Se)(4) growth and development of high efficiency kesterite solar cells. Efficiencies of 5.5% and 6.4% are obtained using ceramic and SLG substrates respectively (without antireflection coatings and without grids).