Given the success of high-altitude wide-field gamma-ray detectors, such as HAWC and LHAASO, we explore a new gamma-hadron separation variable for the future Southern Wide-field Gamma-ray Observatory (SWGO), currently in the R&D phase. SWGO will be a ground-based, high duty cycle, extensive air shower water Cherenkov detector array with a high fill factor core, expected to be located in the Atacama Astronomical Park, Chile, at an altitude of 4770 m. To identify gamma ray astrophysical sources, primary particles need to be reconstructed from the air showers reaching the detector array using their characteristics to distinguish between gamma rays, considered as signal, and hadrons (i.e. cosmic rays) that are considered background. We use CORSIKA to simulate the development of air showers in the atmosphere up to the arrival of secondary particles at the array of water Cherenkov tanks. We propose the arrival time distribution of secondary particles reaching the detector array as an alternative gamma/hadron separator variable. To evaluate its performance we simulated photons and protons, as primary particles, in the energy range from 1 to 100 TeV for vertical events (i.e. zenith angle = 0°) reaching the center of the array. The optimal separation parameter found, given the above constraints, is the time of the 15% percentile of arriving particles inside a ring of 100 to 150 m. The recognized signal is ≳ 88% on average and the background rejection is ≳ 79%. Nevertheless, the overall time resolution of the tanks, estimated at 3.2 ns, is comparable to the average time separation between photons and protons, which is above 3.7 ns. Consequently, the actual efficiency of this variable is expected to be lower.