Gigantic jets are atmospheric electrical discharges that propagate from the top of thunderclouds to the lower ionosphere. They begin as lightning leaders inside the thundercloud, and the thundercloud charge structure primarily determines if the leader is able to escape upward and form a gigantic jet. No observationally verified studies have been reported on the thundercloud charge structures of the parent storms of gigantic jets. Here we present meteorological observations and lightning simulation results to identify a probable thundercloud charge structure of those storms. The charge structure features a narrow upper charge region that forms near the end of an intense convective pulse. The convective pulse produces strong storm top divergence and turbulence, as indicated by large values of storm top radial velocity differentials and spectrum width. The simulations show the charge structure produces leader trees closely matching observations. This charge structure may occur at brief intervals during a thunderstorm's evolution due to the brief nature of convective pulses, which may explain the rarity of gigantic jets compared to other forms of atmospheric electrical discharges.