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Reconstructing the galaxy peculiar velocity field from the distribution oflarge-scale structure plays an important role in cosmology. On one hand, itgives us an insight into structure formation and gravity; on the other, itallows us to selectively extract the kinetic Sunyaev-Zeldovich (kSZ) effectfrom cosmic microwave background (CMB) maps. In this work, we employhigh-accuracy synthetic galaxy catalogs on the light cone to investigate howwell we can recover the velocity field when utilizing the three-dimensionalspatial distribution of the galaxies in a modern large-scale structureexperiment such as the Dark Energy Spectroscopic Instrument (DESI) and RubinObservatory (LSST). In particular, we adopt the standard technique used inbaryon acoustic oscillation (BAO) analysis for reconstructing the Zeldovichdisplacements of galaxies through the continuity equation, which yields afirst-order approximation to their large-scale velocities. We investigatevariations in the number density, bias, mask, area, redshift noise, and surveydepth, and smoothing. Since our main goal is to provide guidance for plannedkSZ analysis between DESI and the Atacama Cosmology Telescope (ACT), we applyvelocity reconstruction to a faithful representation of DESI spectroscopic andphotometric targets. We report the cross-correlation coefficient between thereconstructed and the true velocities along the line of sight. For the DESI Y1spectroscopic survey, we expect the correlation coefficient to be $r \approx0.64$, while for a photometric survey with $\sigma_z/(1+z) = 0.02$, as isapproximately the case for the Legacy Survey used in the target selection ofDESI galaxies, $r$ shrinks by half to $r \approx 0.31$. We hope the results inthis paper can be used to inform future kSZ stacking studies. All scripts usedin this paper can be found here:\url{https://github.com/boryanah/abacus_kSZ_recon}.

Velocity reconstruction in the era of DESI and Rubin (part II): Realistic samples on the light cone