In this study, we follow the diffusion and buildup of occupancy of the substrate ceftriaxone in $M. tuberculosis$ β-lactamase BlaC microcrystals by structural analysis of the enzyme substrate complex at single millisecond time resolution. We also show the binding and the reaction of an inhibitor, sulbactam, on a slower millisecond time scale. We use the ‘mix-and-inject’ technique to initiate these reactions by diffusion, and determine the resulting structures by serial crystallography using ultrafast, intense X-ray pulses from the European XFEL (EuXFEL) arriving at MHz repetition rates. Here, we show how to use the EuXFEL pulse structure to dramatically increase the size of the data set and thereby the quality and time resolution of “molecular movies” which unravel ligand binding and enzymatically catalyzed reactions. This shows the great potential for the EuXFEL as a tool for biomedically relevant research, particularly, as shown here, for investigating bacterial antibiotic resistance.