Commissioning of the PADME experiment with a positron beam

The PADME experiment is designed to search for a hypothetical dark photon $A^{\prime}$ produced in positron-electron annihilation using a bunched positron beam at the Beam Test Facility of the INFN Laboratori Nazionali di Frascati. The expected sensitivity to the $A^{\prime}$-photon mixing parameter $\epsilon$ is 10$^{-3}$, for $A^{\prime}$ mass $\le$ 23.5 MeV/$c^{2}$ after collecting $\sim 10^{13}$ positrons-on-target. This paper presents the PADME detector status after commissioning in July 2019. In addition, the software algorithms employed to reconstruct physics objects, such as photons and charged particles, and the calibration procedures adopted are illustrated in detail. The results show that the experimental apparatus reaches the design performance, and is able to identify and measure standard electromagnetic processes, such as positron Bremsstrahlung, electron-positron annihilation into two photons.