We demonstrate the reconstruction of battery electrochemical impedance spectroscopy (EIS) curves from time-domain pulse testing and the distribution of relaxation times (DRT) analysis. In the proposed approach, the DRT directly utilizes measured current data instead of simulated current patterns, thereby enhancing robustness against current variations and data anomalies. The method is demonstrated with a simulation, a single cylindrical battery cell experiment, and an experimental EIS of a completely assembled module of 448 cells. For the 3.7 kWh battery module, we applied a transient current pulse and analyzed the dynamic voltage responses. The EIS curves were reconstructed with DRT and compared to experiments across different states of charge (SoC). The experimental EIS data were corrected by a multistep calibration workflow in a frequency range from 50 mHz to 1 kHz, achieving error corrections of up to 80% at 1 kHz. The reconstructed impedances from the pulse test data are in good agreement with the EIS experiments in a broad frequency range, delivering relevant electrochemical information including the ohmic resistance and dynamic time constants of a battery module and its corresponding submodules. With the proposed workflow, rapid pulse tests can be used for extracting electrochemical information faster than standard EIS, with a 67% reduction in measurement time. This time-domain pulsing approach provides an alternative to EIS characterization, making it particularly valuable for battery monitoring, the classification of battery packs upon their return to the manufacturer, second-life applications, and recycling.