This paper introduces a growth method—suboxide molecular-beam epitaxy (S-MBE)—which enables a drastic enhancement in the growth rates of Ga2O3 and related materials to over 1 μm h−1 in an adsorption-controlled regime, combined with excellent crystallinity. Using a Ga + Ga2O3 mixture with an oxygen mole fraction of x(O) = 0.4 as an MBE source, we overcome kinetic limits that had previously hampered the adsorption-controlled growth of Ga2O3 by MBE. We present growth rates up to 1.6 μm h−1 and 1.5 μm h−1 for Ga2O3/Al2O3 and Ga2O3/Ga2O3 structures, respectively, with very high crystalline quality at unparalleled low growth temperature for this level of perfection. We combine thermodynamic knowledge of how to create molecular beams of targeted suboxides with a kinetic model developed for the S-MBE of III–VI compounds to identify appropriate growth conditions. Using S-MBE, we demonstrate the growth of phase-pure, smooth, and high-purity homoepitaxial Ga2O3 films that are thicker than 4.5 μm. With the high growth rate of S-MBE, we anticipate a significant improvement to vertical Ga2O3-based devices. We describe and demonstrate how this growth method can be applied to a wide range of oxides. With respect to growth rates and crystalline quality, S-MBE rivals leading synthesis methods currently used for the production of Ga2O3-based devices.