Context. The new generation of optical spectrographs, including WEAVE, 4MOST, DESI, and WST, offers huge multiplexing capabilities and excellent spectral resolution. This is an unprecedented opportunity to statistically unveil the details of the star formation histories (SFHs) of galaxies. However, these observations are not easily comparable with the predictions of cosmological simulations. Aims. Our goal is to build a reference framework for comparing spectroscopic observations with cosmological simulations and to test the currently available tools for deriving the stellar population properties of mock galaxies as well as their SFHs. We focus on the observational strategy of the Stellar Population at intermediate redshift Survey (StePS) carried out with the WEAVE instrument. Methods. We created mock datasets of ∼750 galaxies at redshifts of z = 0.3, 0.5, and 0.7 from the TNG50 cosmological simulation. We performed radiative transfer calculations using SKIRT and analyzed the spectra with the pPXF algorithm, treating them as if they were real observations. Results. This work presents the methodology used to generate the mock datasets, providing an initial exploration of stellar population properties (i.e. mass-weighted ages and metallicities) and SFHs of a test sample of three galaxies at z = 0.7 and their descendants at z = 0.5 and 0.3. We show that there is very good agreement between mock WEAVE-like spectra compared to the intrinsic values in TNG50 (average difference of 0.2 ± 0.3 Gyr). We also report that an overall agreement is seen when retrieving the SFHs of galaxies, especially if they form the bulk of their stars on short timescales and at early epochs. While we did identify a tendency to overestimate the weight of old stellar populations in galaxies with complex SFHs, we were able to properly recover the timescales on which galaxies build up 90% of their mass, with almost no difference in the measured and intrinsic cumulative SFHs over the last 4 Gyr. Conclusions. We have released the datasets concurrently with this publication of this paper, which consist of multi-wavelength imaging and spectroscopic data of ∼750 galaxies at redshift z = 0.3, 0.5, and 0.7. This work provides a fundamental bench-test for forthcoming WEAVE observations, providing the community with realistic mock spectra of galaxies that can be used to test currently available tools for deriving first-order stellar populations parameters (i.e. ages and metallicities) as well as more complex diagnostics, such as mass and SFHs.