The magnetic proximity effect is one of the powerful approaches to realize quantum anomalous Hall effect in topological insulators (TIs) targeting at high temperatures. Various TI/ferromagnetic-insulator (FMI) heterostructures have extensively been investigated by using a van der Waals epitaxial growth technique of TI films grown on FMI substrates. However, FMI materials which can be used as a substrate are strictly limited due to the lattice mismatching between TI and FMI, not succeeding to boost the quantization temperature to be higher. Here, we show that a large anomalous Hall effect, comparable to the best value so far reported for the heterostructure interfaces fabricated by epitaxial growth techniques, is realized for Bi1.5Sb0.5Te1.7Se1.3 (BSTS)/Cr2Ge2Te6 (CGT) heterostructure by transferring an epitaxially grown BSTS thin film floating on a ultrapure water directly on a CGT substrate (wet transfer method). The fundamental discussions about the nature of magnetic proximity effect were given in the aspect of the quality of the CGT substrate and the atomic orientation of the TI/CGT interface. The large magnetic proximity effect shown in our present studies can be applicable for a variety of FMI substrates and therefore can pave a route for promoting magnetic TIs both in basic science and applications.