Terrestrial Gamma-ray flashes (TGFs) are bursts of gamma-rays initiated in the Earth’s atmosphere by atmospheric lightning. The Terrestrial Gamma-ray flashes discussed in this work were detected at ground level between 2014 and 2018, by the Telescope Array Surface Detector (TASD), a lightning mapping array installed in 2013, and a broadband interferometer and fast sferics sensor installed in 2018. The TASD is a 700 square kilometer ultra high energy cosmic ray detector in the southwestern desert of Utah, U.S.A. It is composed of 507 (3 square meter) plastic scintillator detectors on a 1.2 km square grid. In 2013, a Lightning Mapping Array (LMA) detector and a Slow antenna (SA) were installed at the TASD site. The LMA is a three-dimensional total lightning location system, comprised of nine stations located within and around the TASD array. The SA records the electric field change in lightning discharges. The TASD has become one of the world leading instruments for detection of TGFs from the ground. The downward Gamma-ray showers observed by the TASD detector were all confined to the first 1-2 ms of intracloud and cloud to ground discharges, spanning an overall duration of several hundreds of microseconds. We hypothesize that the observed TGFs are similar to those detected by satellites, but that the TASD ground-based observations are able to detect both the temporal distribution at the source and the full footprint of the gamma shower on the ground. More importantly, the gamma ray bursts observations suggest that the TGFs were produced by one or two particularly energetic leader steps at the initial breakdown pulse (IBP) stage. To confirm such correspondence, an interferometer (INTF) and a fast antenna were installed a few kilometers east of the TASD detector on July 2018. With these additional lightning detection instruments in concert with the TASD cosmic ray observatory, LMA, and SA, we are able, to present, for the first time, observations of the TGFs clearly associated with the IBPs of downward cloud-to-ground flashes and intracloud flashes. This result sheds new light on the origins of Terrestrial Gamma-ray Flashes.