Nonthermal sources located above bright flare arcades, referred to as the above-the-loop-top sources, have been often suggested as the primary electron acceleration site in major solar flares. The X8.2 limb flare on 2017 September 10 features such an above-the-loop-top source, which was observed in both microwaves and hard X-rays (HXRs) by the Expanded Owens Valley Solar Array (EOVSA) and the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI), respectively. By combining the microwave and HXR imaging spectroscopy observations with multi-filter extreme ultraviolet and soft X-ray imaging data, we derive the energetic electron distribution of this source over a broad energy range from $<$10 keV up to $sim$MeV during the early impulsive phase of the flare. The best-fit electron distribution consists of a thermal core from $sim$25 MK plasma. Meanwhile, a nonthermal power-law tail joins the thermal core at $sim$16 keV with a spectral index of $sim$3.6, which breaks down at above $sim$160 keV to $>$6.0. In addition, temporally resolved analysis suggests that the electron distribution above the break energy rapidly hardens with the spectral index decreasing from $>$20 to $sim$6.0 within 20 s, or less than $sim$10 Alfv{e}n crossing times in the source. These results provide strong support for the above-the-loop-top source as the primary site where an on-going bulk acceleration of energetic electrons is taking place very early in the flare energy release.
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