The oxidation-related issues in controlling Si doping from the Si source material in oxide molecular beam epitaxy (MBE) are addressed by using its solid suboxide, SiO, as an alternative source material in a conventional effusion cell. Line-of-sight quadrupole mass spectrometry of the direct SiO-flux (ΦSiO) from the source at different temperatures (TSiO) confirmed SiO molecules to sublime with an activation energy of 3.3 eV. The TSiO-dependent ΦSiO was measured in vacuum before and after subjecting the source material to an O2-background of 10−5 mbar (typical oxide MBE regime). The absence of a significant ΦSiO difference indicates negligible source oxidation in molecular O2. Mounted in an oxygen plasma-assisted MBE, Si-doped β-Ga2O3 layers were grown using this source. The ΦSiO at the substrate was evaluated [from 2.9 × 109 cm−2 s−1 (TSiO = 700 °C) to 5.5 × 1013 cm−2 s−1 (TSiO = 1000 °C)] and Si-concentration in the β-Ga2O3 layers measured by secondary ion mass spectrometry highlighting unprecedented control of continuous Si-doping for oxide MBE, i.e., NSi from 4 × 1017 cm−3 (TSiO = 700 °C) up to 1.7 × 1020 cm−3 (TSiO = 900 °C). For a homoepitaxial β-Ga2O3 layer, a Hall charge carrier concentration of 3 × 1019 cm−3 in line with the provided ΦSiO (TSiO = 800 °C) is demonstrated. No SiO-incorporation difference was found between β-Ga2O3(010) layers homoepitaxially grown at 750 °C and β-Ga2O3(−201) heteroepitaxial layers grown at 550 °C on c-plane sapphire. However, the presence of activated oxygen (plasma) resulted in partial source oxidation and related decrease in doping concentration (particularly at TSiO < 800 °C), which has been tentatively explained with a simple model. Degassing the source at 1100 °C reverted this oxidation. Concepts to reduce source oxidation during MBE-growth are referenced.