We report the first search result for the flux of astrophysical electron antineutrinos for energies (10)MeV in the gadolinium-loaded Super-Kamiokande (SK) detector. In 2020 June, gadolinium was introduced to the ultrapure water of the SK detector in order to detect neutrons more efficiently. In this new experimental phase, SK-Gd, we can search for electron antineutrinos via inverse beta decay with efficient background rejection thanks to the high efficiency of the neutron tagging technique. In this paper, we report the result for the initial stage of SK-Gd, during 2020 August 26, and 2022 June 1 with a 22.5 × 552 kton · day exposure at 0.01% Gd mass concentration. No significant excess over the expected background in the observed events is found for the neutrino energies below 31.3 MeV. Thus, the flux upper limits are placed at the 90% confidence level. The limits and sensitivities are already comparable with the previous SK result with pure water (22.5 × 2970 kton · day) owing to the enhanced neutron tagging. Operation with Gd increased to 0.03% started in 2022 June.