The SRG/eROSITA All-Sky Survey (eRASS) allows for the creation of a complete sample of X-ray dim isolated neutron stars (XDINSs), which will significantly facilitate the study of their population properties, evolution, and connection to other families of isolated neutron stars (INSs). In this work, we conduct a systematic search for XDINSs on the eROSITA western Galactic hemisphere down to an X-ray flux limit of 10⁻¹³ erg s⁻¹ cm⁻² and discuss the resulting candidate sample. Consistently with the properties of the known XDINSs, we selected all eRASS sources possessing a soft X-ray spectral distribution and that are unlikely to be associated with optical or infrared sources. Our selection criteria allowed us to recover all known XDINSs and previously proposed candidates. In addition, we put forward 33 new candidate members for dedicated follow-up identification campaigns. We found the resulting candidate sample to be about 30–50% complete, mainly due to source confusion and the stringent cross-matching criteria adopted to select the most promising candidates for immediate follow-up investigation. The candidates of the sample presented here can be broadly divided into two groups: 13 rather soft and 20 hot and somewhat hard X-ray emitters. Interestingly, the remarkably thermal nature of the candidates in the first group as well as their spatial distribution, lack of known counterparts, and absence of significant flux variability agree well with the properties of other confirmed thermally emitting INSs. For the candidates in the second group, the current observational data do not allow one to discern between rotation-powered or recycled pulsars, cataclysmic variables, or quiescent neutron stars in binary systems or even to rule out an extragalactic nature. On the basis of population synthesis and the estimated source completeness of the search, we expect that between one and three new XDINSs are among the already singled-out list of XDINS candidates – a long-sought increase in the proposed number of members of this elusive class of X-ray emitters.