Chalcogenide superlattices (SLs), formed by the alternate stacking of GeTe and Sb₂Te₃ layers, also referred to as interfacial phase-change memory (iPCM), are a leading candidate for spin-based memory device applications. Theoretically, the iPCM structure has been predicted to form a three-dimensional topological insulator or Dirac semimetal phase depending on the constituent layer thicknesses. Here, we experimentally investigate the topological insulating nature of chalcogenide SLs using a helicity-dependent time-resolved Kerr measurement. The helicity-dependent Kerr signal is observed to exhibit a four-cycle oscillation with π/2 periodicity, suggesting the existence of a Dirac-like cone in some chalcogenide SLs. Furthermore, we found that increasing the thickness of the GeTe layer dramatically changed the periodicity, indicating a phase transition from a Dirac semimetal into a trivial insulator. Our results demonstrate that thickness-tuned chalcogenide SLs can play an important role in the manipulation of topological states, which may open up new possibilities for spintronic devices based on chalcogenide SLs.