A quantum anomalous Hall (QAH) insulator coupled to an s-wave superconductor is predicted to harbor a topological superconducting phase, the elementary excitations of which (i.e. Majorana fermions) can form topological qubits upon non-Abelian braiding operations. A recent transport experiment interprets the half-quantized two-terminal conductance plateau as the presence of chiral Majorana fermions in a millimeter-size QAH-Nb hybrid structure. However, there are concerns about this interpretation because non-Majorana mechanisms can also generate similar signatures, especially in a disordered QAH system. Here, we fabricated QAH-Nb hybrid structures and studied the QAH-Nb contact transparency and its effect on the corresponding two-terminal conductance. When the QAH film is tuned to the metallic regime by electric gating, we observed a sharp zero-bias enhancement in the differential conductance, up to 80% at zero magnetic field. This large enhancement suggests high probability of Andreev reflection and transparent interface between the magnetic topological insulator (TI) and Nb layers. When the magnetic TI film is in the QAH state with well-aligned magnetization, we found that the two-terminal conductance is always half-quantized. Our experiment provides a comprehensive understanding of the superconducting proximity effect observed in QAH-superconductor hybrid structures and shows that the half-quantized conductance plateau is unlikely to be induced by chiral Majorana fermions.