We experimentally investigate Andreev transport through a single junction between an s-wave indium superconductor and a thick film of a three-dimensional $Bi_2Te_3$ topological insulator. We study $Bi_2Te_3$ samples with different bulk and surface characteristics, where the presence of a topological surface state is confirmed by direct ARPES measurements. All the junctions demonstrate Andreev transport within the superconducting gap. For junctions with transparent $In-Bi_2Te_3$ interfaces we find a number of nearly periodic conductance oscillations, which are accompanied by zero-bias conductance anomaly. Both effects disappear above the superconducting transition or for resistive junctions. We propose a consistent interpretation of both effects as originating from proximity-induced superconducting correlations within the $Bi_2Te_3$ topological surface state.