Abstract: Thermal light dark matter (LDM) with particle masses in the 1 MeV-1 GeV range could successfully explain the observed dark matter abundance as a relic from the primordial Universe. In this picture, a new feeble interaction acts as a “portal” between the Standard Model and LDM particles, allowing for the exploration of this paradigm at accelerator experiments. In the last years, the “missing energy” experiment NA64e at CERN SPS (Super Proton Synchrotron) has set world-leading constraints in the vector-mediated LDM parameter space, by exploiting a 100 GeV electron beam impinging on an electromagnetic calorimeter, acting as an active target. In this paper, we report a detailed description of the analysis of a preliminary measurement with a 70 GeV/c positron beam at NA64e, performed during summer 2023 with an accumulated statistics of 1.596 x 1010 positrons on target (hereafter referred to as e+OT). This data set was analyzed with the primary aim of evaluating the performance of the NA64e detector with a lower energy positron beam, towards the realization of the post-LS3 program. The analysis results, other than additionally probing unexplored regions in the LDM parameter space, provide valuable information towards the future NA64e positron campaign.