KTaO3 heterostructures have recently attracted attention as model systems to study the interplay of quantum paraelectricity, spin-orbit coupling, and superconductivity. However, the high and low vapor pressures of potassium and tantalum present processing challenges to creating heterostructure interfaces clean enough to reveal the intrinsic quantum properties. Here, we report superconducting heterostructures based on high-quality epitaxial (111) KTaO3 thin films using an adsorption-controlled hybrid PLD to overcome the vapor pressure mismatch. Electrical and structural characterizations reveal that the higher-quality heterostructure interface between amorphous LaAlO3 and KTaO3 thin films supports a two-dimensional electron gas with substantially higher electron mobility, superconducting transition temperature, and critical current density than that in bulk single-crystal KTaO3-based heterostructures. Our hybrid approach may enable epitaxial growth of other alkali metal-based oxides that lie beyond the capabilities of conventional methods.