Earth system reanalysis datasets are foundational for weather and climate research and provide the gridded training data used by most machine learning weather prediction systems. Here we show results from a prototype system that suggest that machine learning models trained only on Earth system observations can potentially be used to generate multi-decade global reanalyses without using physics-based numerical models. The resulting gridded fields capture large-scale atmospheric structure and variability across multiple timescales, while exhibiting signs of physical coherence in several key dynamical diagnostics. Evaluations of the prototype against held-out independent atmospheric observations indicate that the root mean square vector error of upper-level winds is close to that of ERA5 when compared at a consistent resolution, and that the standard deviation of the error at the surface is between that of 4th- and 5th-generation ECMWF reanalyses (ERA-Interim and ERA5). Furthermore, while traditional reanalysis production is computationally expensive, typically taking several years to produce, the reanalysis presented here was generated during the course of a single working day. These results suggest that observation-trained machine learning models offer a promising new approach for reanalysis production from observations alone.