Hydrogen 21-cm Line Intensity Mapping offers the unique opportunity to access the Dark Ages and trace the formation and evolution of the large scale structure of the Universe prior to star and galaxy formation. In this work we investigate the potential of future Earth- and Moon-based 21-cm surveys to constrain the growth of structures during the currently unexplored redshift range 30 < z < 200. On the one hand we show how foreground contamination could limit the capabilities of future instruments in achieving precision below the 10% level. On the other hand, observations from the far side of the Moon have the potential to reach percent or even sub-percent precision in terms of reconstructing the growth of cosmic structures, if foregrounds are robustly accounted for. Such exquisite precision will provide tight constraints on models that induce deviations from ΛCDM, not only during the Dark Ages, but also during recombination or that manifest mostly in the low-redshift Universe, like Early Dark Energy and nDGP models, respectively. Thus, because of their insensitivity to non-linearities or astrophysical processes, line intensity mapping surveys will provide a formidable consistency check to potential claims of discoveries of new physics that affect the growth of structures.