Two-dimensional topological insulators (2DTIs) or quantum spin Hall insulators are attracting increasing attention due to their potential applications in next-generation spintronic devices. Despite their promising prospects, realizable 2DTIs are still limited. Recently, Ta2Pd3Te5, a semiconducting van der Waals material, has shown spectroscopic evidence of quantum spin Hall states. However, achieving controlled preparation of few- to monolayer samples, a crucial step in realizing quantum spin Hall devices, has not yet been achieved. In this work, we fabricated few- to monolayer Ta$_2$Pd$_3$Te$_5$ and performed systematic thickness- and temperature-dependent Raman spectroscopy measurements. Our results demonstrate that Raman spectra can provide valuable information to determine the thickness of Ta2Pd3Te5 thin flakes. Moreover, our angle-resolved polarized Raman (ARPR) spectroscopy measurements show that the intensities of the Raman peaks are strongly anisotropic due to the quasi-one-dimensional atomic structure, providing a straightforward method to determine its crystalline orientation. Our findings may stimulate further efforts to realize quantum devices based on few or monolayer Ta$_2$Pd$_3$Te$_5$.