We present a suite of high-resolution cosmological zoom-in simulations to z = 4 of a 1012 M⊙ halo at z = 0, obtained using seven contemporary astrophysical simulation codes (Art-I, Enzo, Ramses, Changa, Gadget-3, Gear, and Gizmo) widely used in the numerical galaxy formation community. The physics prescriptions for gas cooling and heating and star formation are the same as the ones used in our previous Assembling Galaxies of Resolved Anatomy (AGORA) disk comparison but now account for the effects of cosmological processes such as the expansion of the universe, intergalactic gas inflow, and the cosmic ultraviolet background radiation emitted by massive stars and quasars. In this work, we introduce the most careful comparison yet of galaxy formation simulations run by different code groups, together with a series of four calibration steps each of which is designed to reduce the number of tunable simulation parameters adopted in the final run. In the first two steps, we methodically calibrate the gas physics, such as cooling and heating, in simulations without star formation. In the third step, we seek agreement on the total stellar mass produced with the common star formation prescription used in the AGORA disk comparison, in stellar-feedback-free simulations. In the last calibration step, we activate stellar feedback, where each code group is asked to set the feedback prescription to as close to the most widely used one in its code community as possible, while aiming for convergence in the stellar mass at z = 4 to the values predicted by semiempirical models. After all the participating code groups successfully complete the calibration steps, we achieve a suite of cosmological simulations with similar mass assembly histories down to z = 4. With numerical accuracy that resolves the internal structure of a target halo (≲100 physical pc at z = 4), we find that the codes overall agree well with one another, e.g., in gas and stellar properties, but also show differences, e.g., in circumgalactic medium (CGM) properties. We argue that, if adequately tested in accordance with our proposed calibration steps and common parameters, high-resolution cosmological zoom-in simulations can have robust and reproducible results. New code groups are invited to join and enrich this comparison by generating equivalent models or to test the code's compatibility on their own, by adopting the common initial conditions, the common easy-to-implement physics package, and the proposed calibration steps. Further analyses of the zoom-in simulations presented here will be presented in forthcoming reports from the AGORA Collaboration, including studies of the CGM, simulations by additional codes, and results at lower redshift.