Abstract Obscuration of quasars by accreted gas and dust, or dusty intervening galaxies, can cause active galactic nuclei (AGN) to be missed in optically-selected surveys. Radio observations can overcome this dust bias. In particular, radio surveys searching for H i absorption inform us on how the AGN can impact on the cold neutral gas medium within the host galaxy, or the population of intervening galaxies through the observed line of sight gas kinematics. We present the results of a H i absorption line survey at 0.4 < z < 1 towards 34 obscured quasars with the Australian SKA Pathfinder (ASKAP) commissioning array. We detect three H i absorption lines, with one of these systems previously unknown. Through optical follow-up for two sources, we find that in all detections the H i gas is associated with the AGN, and hence that these AGN are obscured by material within their host galaxies. Most of our sample are compact, and in addition, are either gigahertz peaked spectrum (GPS), or steep spectrum (CSS) sources, both thought to represent young or recently re-triggered radio AGN. The radio spectral energy distribution classifications for our sample agree with galaxy evolution models in which the obscured AGN has only recently become active. Our associated H i detection rate for GPS and compact SS sources matches those of other surveys towards such sources. We also find shallow and asymmetric H i absorption features, which agrees with previous findings that the cold neutral medium in compact radio galaxies is typically kinematically disturbed by the AGN.