The Galactic Center (GC) has the largest concentration and highest number density of stars within the Galaxy. We demonstrate that a line-of-sight towards the GC offers the largest integrated Galactic star count and the largest number of potentially habitable systems of any direction in the sky. The GC also offers an ideal Schelling point to place a powerful transmitter to efficiently send beacons across the entire Milky Way. The Breakthrough Listen program is undertaking a comprehensive survey of the GC, which will be one of the most sensitive and deepest targeted SETI surveys ever conducted. In this paper, we outline our observing strategies to search a large fraction of the accessible radio-window— from 0.7 GHz to 93 GHz—to conduct a deep survey of the GC and the surrounding bulge region using two of the world’s most powerful radio telescopes: the Robert C. Byrd Green Bank Telescope and Parkes Telescope, with a total of around 600 hours of observing. We report preliminary results from our survey for ETI beacons across 1–8 GHz with 7.0 hours and 11.2 hours of observing with Parkes and GBT, respectively. With our narrowband drifting signal search, we are able to reject the presence of strong transmitters at the GC and in around 60 million stars across 1–4.0 GHz with an EIRP limit of ≥4×1018 W, and around half a million stars across 3.95–8 GHz with an EIRP limit of ≥5×1017 W, which is equivalent to the energy budget of Kardashev Type I societies. For the first time, we were able to constrain the existence of artificially dispersed transient signals (negative DM) across 3.95–8 GHz, emanating from strong ETI beacons located at the GC with EIRP ≥1×1014 W/Hz with a repetition period ≤4.3 hours. Our survey also allowed searches for astrophysical transients such as Fast Radio Burst-like magnetars near the GC at 6 GHz. We searched our 11.2 h of deep observations of the GC and its surrounding region for such transient bursts up to the DM of 5000 pc cm−3 with maximum pulse widths up to 90 ms. We detected several hundred transient bursts from SGR J1745−2900, but did not detect any new transient signal with the peak luminosity limit across our observed band of ≥1031 erg s−1 and burst-rate of ≥0.23 burst-hr−1 for a source located at the GC. These limits are comparable to bright transient emission seen from other Galactic radio-loud magnetars.