The computational analysis of transient wave propagation in large-scale three-dimensional domains presents a significant challenge due to the stringent spatial discretization requirements imposed by stability and accuracy constraints. Conventional finite element approaches necessitate uniformly fine meshes across the entire domain throughout the simulation, resulting in prohibitive computational costs as the vast majority of elements remain inactive outside the localized wavefront region. To address this difficulty, this paper introduces a novel, efficient computational framework that overcomes this inefficiency through dynamic, wavefront-tracking mesh adaptation. The proposed methodology synergistically combines the Scaled Boundary Finite Element Method (SBFEM) with a hierarchical octree discretization strategy. Simulations initiates with a coarse base mesh and a strain-energy-based error indicator enables an automated local refinement strategy exclusively within the advancing wavefront region. A local coarsening of the mesh is implemented after the wavefront passes, enabling optimal computational resource utilization. The proposed strategy exploits the salient feature of SBFEM: the intrinsic compatibility with arbitrary polyhedral elements, permitting direct treatment of the hanging nodes generated by octree refinement without auxiliary constraints. Numerical benchmarks in 3D elastodynamics demonstrate that the adaptive framework reduces the active degrees of freedom significantly compared to static fine-mesh simulations, while preserving accuracy and stability. This work establishes a new paradigm for computationally tractable, high-fidelity wave simulations in applications including seismic analysis, non-destructive testing, and vibroacoustic simulation.