Context. The Spectrometer/Telescope for Imaging X-rays (STIX) is the hard X-ray instrument onboard Solar Orbiter designed to observe solar flares over a broad range of flare sizes. Aims. We report the first STIX observations of solar microflares recorded during the instrument commissioning phase in order to investigate the STIX performance at its detection limit. Methods. STIX uses hard X-ray imaging spectroscopy in the range between 4–150 keV to diagnose the hottest flare plasma and related nonthermal electrons. This first result paper focuses on the temporal and spectral evolution of STIX microflares occuring in the Active Region (AR) AR12765 in June 2020, and compares the STIX measurements with Earth-orbiting observatories such as the X-ray Sensor of the Geostationary Operational Environmental Satellite (GOES/XRS), the Atmospheric Imaging Assembly of the Solar Dynamics Observatory, and the X-ray Telescope of the Hinode mission. Results. For the observed microflares of the GOES A and B class, the STIX peak time at lowest energies is located in the impulsive phase of the flares, well before the GOES peak time. Such a behavior can either be explained by the higher sensitivity of STIX to higher temperatures compared to GOES, or due to the existence of a nonthermal component reaching down to low energies. The interpretation is inconclusive due to limited counting statistics for all but the largest flare in our sample. For this largest flare, the low-energy peak time is clearly due to thermal emission, and the nonthermal component seen at higher energies occurs even earlier. This suggests that the classic thermal explanation might also be favored for the majority of the smaller flares. In combination with EUV and soft X-ray observations, STIX corroborates earlier findings that an isothermal assumption is of limited validity. Future diagnostic efforts should focus on multi-wavelength studies to derive differential emission measure distributions over a wide range of temperatures to accurately describe the energetics of solar flares. Conclusions. Commissioning observations confirm that STIX is working as designed. As a rule of thumb, STIX detects flares as small as the GOES A class. For flares above the GOES B class, detailed spectral and imaging analyses can be performed.