Enzymatic hydrolysis of lactose is a crucial step to improve the efficiency and selectivity of membrane-based separations toward the recovery of milk oligosaccharides free from simple sugars. Response surface methodology was used to investigate the effects temperature (25.9 to 54.1 °C) and amount of enzyme (0.17 to 0.32% w/w) at 1, 2, and 4 h of reaction on the efficiency of lactose hydrolysis by Aspergillus oryzae β-galactosidase, preservation of major goat whey oligosaccharides, and on the de-novo formation of oligosaccharides. Lactose hydrolysis above 99% was achieved at 1, 2, and 4 h, not being significantly affected by temperature and amount of enzyme within the tested conditions. Formation of 4 Hexose (Hex) and 4 Hex 1 Hex and an increased de-novo formation of 2 Hex 1 N-Acetyl-Neuraminic Acid (NeuAc) and 2 Hex 1 N-Glycolylneuraminic acid (NeuGc) was observed in all treatments. Overall, processing conditions using temperatures ≤40 °C and enzyme concentration ≤0.25% resulted in higher preservation/formation of goat whey oligosaccharides.