Prediction of ground motion triggered by earthquakes is a prime concern for both the seismology community and geotechnical earthquake engineering one. The subfield occupied with such a problem is termed site response analysis (SRA), its one-dimensional flavor (1D-SRA) being particularly popular given its simplicity. Despite the simple geometrical setting, a paramount challenge remains when it comes to numerically consider intense shaking in the soft upper soil strata of the crust: how to mathematically model the high-strain, dissipative, potentially rate-dependent soil behavior. Both heuristics models and phenomenological constitutive laws have been developed to meet the challenge, neither of them being exempt of either numerical limitations or physical inadequacies or both. We propose herein to bring the novel data-driven paradigm to bear, thus giving away with the need to construct constitutive behavior models altogether. Data-driven computational mechanics (DDCM) is a novel paradigm in solid mechanics that is gaining popularity; in particular, the multiscale version of it relies on studying the response of the microstructure (in the case of soil, representative volumes containing grains) to populate a dataset that is later used to inform the response at the macroscale. This manuscript presents the first application of multiscale DDCM to 1D-SRA: first, we demonstrate its capacity to handle wave propagation problems using discrete datasets, obtained via sampling grain ensembles using the discrete element method (DEM), in lieu of a constitutive law and then we apply it specifically to analyze the propagation of harmonic waves in a soft soil deposit that overlies rigid bedrock. We validate the implementation via comparison to regular finite elements analyses (FEA) and demonstrate that traditional amplification functions are recovered when using the DDCM. 14 pages, 7 figures