The first observation of the singly Cabibbo-suppressed Ω0 c → Ω−K+ and Ω0 c → Ξ−π+ decays is reported, using proton-proton collision data at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 5.4 fb−1, collected with the LHCb detector between 2016 and 2018. The branching fraction ratios are measured to be B(Ω0 c → Ω−K+) B(Ω0 c → Ω−π+) = 0.0608 ± 0.0051 (stat) ± 0.0040 (syst), B(Ω0 c → Ξ−π+) B(Ω0 c → Ω−π+) = 0.1581 ± 0.0087 (stat) ± 0.0043 (syst) ± 0.0016 (ext). In addition, using the Ω0 c → Ω−π+ decay channel, the Ω0 c baryon mass is measured to be M (Ω0 c ) = 2695.28 ± 0.07 (stat) ± 0.27 (syst) ± 0.30 (ext) MeV/c2, improving the precision of the previous world average by a factor of four.