Inspired by concepts developed for fermionic systems in the framework of condensed matter physics, topology and topological states are recently being explored also in bosonic systems. Recently, some of these concepts have been successfully applied to acoustic phonons in nanoscale multilayered systems. The reported demonstration of confined topological phononic modes was based on Raman scattering spectroscopy [M. Esmann et al., Phys. Rev. B 97, 155422 (2018)], yet the resolution did not suffice to determine lifetimes and to identify other acoustic modes in the system. Here, we use time-resolved pump-probe measurements using an asynchronous optical sampling (ASOPS) technique to overcome these resolution limitations. By means of one-dimensional GaAs/AlAs distributed Bragg reflectors (DBRs) used as building blocks, we engineer high frequency (∼200 GHz) topological acoustic interface states. We are able to clearly distinguish confined topological states from stationary band edge modes. The generation/detection scheme reflects the symmetry of the modes directly through the selection rules, evidencing the topological nature of the measured confined state. These experiments enable a new tool in the study of the more complex topology-driven phonon dynamics such as phonon nonlinearities and optomechanical systems with simultaneous confinement of light and sound.