Aims: We present a new method that investigates the evolutionary history of the pulsating DB white dwarf GD 358 using asteroseismology. This is done considering the internal C/O profile, which describes the relative abundances of carbon and oxygen from the core of the star to its surface. Different evolutionary channels lead to the generation of different C/O profiles, and these affect the pulsation periods. Methods: We used the C/O profiles associated with white dwarfs that evolved through binary evolution channels where the progenitor experienced one or two episodes of mass loss during one or two common envelope (CE) phases, and two profiles from single-star evolution. We computed models using these different profiles and used a genetic algorithm (GA) to optimize the search in the parameter space for the best fit to the observed pulsation periods. We used three-parameter models, adjusting the stellar mass (Mstar), the effective temperature (T_eff), and the helium mass of the external layer (M_He). Results: Our results suggest that binary evolution profiles may provide a better match to the pulsation periods of GD 358. The best fit to the observations is obtained using a profile related to an evolutionary history where two episodes of mass loss happen during two CE phases, the first during the RGB (red giant branch) stage. The values obtained are T_eff = 24300 K, Mstar = 0.585 M&sun;, and log (M_He/Mstar) = -5.66. The best-fit model has a mass close to the mean mass for DB white dwarfs found in various works and a temperature consistent with UV spectra obtained with the IUE satellite.