Electron beam accelerators are essential in many scientific and technological fields. Their operation relies heavily on the stability and precision of the electron beam. Traditional diagnostic techniques encounter difficulties in addressing the complex and dynamic nature of electron beams. Particularly in the context of free-electron lasers (FELs), it is fundamentally impossible to measure the lasing-on and lasing-off electron power profiles for a single electron bunch. This is a crucial hurdle in the exact reconstruction of the photon pulse profile. To overcome this hurdle, we developed a machine learning model that predicts the temporal power profile of the electron bunch in the lasing-off regime using 22 machine parameters. The model was statistically validated and showed superior predictions compared to the state-of-the-art batch calibrations. This is a critical element for a virtual pulse reconstruction diagnostic (VPRD) tool designed to reconstruct the power profile of individual photon pulses without requiring repeated measurements in the lasing-off regime. This promises to significantly enhance the diagnostic capabilities in FELs at large.