During its 6-year nominal mission, Euclid shall survey one third of the sky, enabling us to examine the spatial distributions of dark and luminous matter during the past 10 Gyr of cosmic history. The Euclid satellite was successfully launched on a SpaceX Falcon 9 launcher from Cape Canaveral on 1 July 2023 and is fully operational in a halo orbit around the Second Sun-Earth Lagrange point. We present an overview of the expected and unexpected findings during the early phases of the mission, in the context of technological heritage and lessons learnt. The first months of the mission were dedicated to the commissioning of the spacecraft, telescope and instruments, followed by a phase to verify the scientific performance and to carry out the in-orbit calibrations. We report that the key enabling scientific elements, the 1.2-meter telescope and the two scientific instruments, a visual imager (VIS) and a near-infrared spectrometer and photometer (NISP), show an in-orbit performance in line with the expectations from ground tests. The scientific analysis of the observations from the Early Release Observations (ERO) program done before the start of the nominal mission showed sensitivities better than the pre-launch requirements. The nominal mission started in December 2023, and we allocated a 6-month early survey operations phase to closely monitor the performance of the sky survey. We conclude with an outlook of the activities for the remaining mission in the light of the in-orbit performance.
