In the concordance cosmological scenario, the cold collisionless dark matter component dominates the mass budget of galaxies and interacts with baryons only via gravity. However, there is growing evidence that the former, instead, responds to the baryonic (feedback) processes by modifying its density distribution. These processes can be captured by comparing the inner dynamics of galaxies across cosmic time. We present a pilot study of dynamical mass modeling of high redshift galaxy rotation curves, which is capable of constraining the structure of dark matter halos across cosmic time. We investigate the dark matter halos of 256 star-forming disk-like galaxies at z~1 using the KMOS Redshift One Spectroscopic Survey (KROSS). This sample covers the redshifts 0.6<=z<=1.04, effective radii 0.69<=Re[kpc]<=7.76, and total stellar masses 8.7<=log(Mstar [M])<=11.32. We present a mass modeling approach to study the rotation curves of these galaxies, which allow us to dynamically calculate the physical properties associated with the baryons and the dark matter halo. For the former we assume a Freeman disk, while for the latter we employ the NFW (cusp) and the Burkert (cored) halo profiles, separately. At the end, we compare the results of both cases with state-of-the-art galaxy simulations (EAGLE, TNG100, and TNG50). We find that the "cored" dark matter halo emerged as the dominant quantity from a radius 1-3 times the effective radius. Its fraction to the total mass is in good agreement with the outcome of hydrodynamical galaxy simulations. Remarkably, we found that the dark matter core of z~1 star-forming galaxies are smaller and denser than their local counterparts. Dark matter halos have gradually expanded over the past 6.5Gyrs. That is, observations are capable of capturing the dark matter response to the baryonic processes, thus giving us the first piece of empirical evidence of "gravitational potential fluctuations" in the inner region of galaxies that can be verified with deep surveys and future missions.