Silicon heterojunction (SHJ) solar cells are recognized as one of the most efficient architectures in silicon-based photovoltaic devices. However, the reliance on indium (In)-based transparent conductive oxides (TCO) is anticipated to constrain their production capacity due to the critical and economically volatile nature of In. Recently, low-temperature-grown amorphous SnO2 (a-SnO2) films have been explored as an earth-abundant alternative TCO material. In this study, we examine the electrical contact properties of a-SnO2 layers employed as TCO layers in SHJ cells, focusing on their interaction with the underlying carrier selective contact layers. Our findings indicate that a stack of doped amorphous silicon (a-Si:H) and a-SnO2 exhibits relatively high specific contact resistivity, leading to a significant reduction in the device's fill factor. To address this issue, we propose two approaches: the insertion of a thin ZnO-based TCO layer between a-Si:H and a-SnO2, and the use of nanocrystalline silicon layers in place of a-Si:H. Both approaches effectively reduce the contact resistivity, resulting in improvements in fill factor and conversion efficiency comparable to those of benchmark device with In-based TCOs. Based on these findings, we demonstrate a high-efficiency, In-free, SnO2-based SHJ cell.