Offline reference trajectories for active target tracking are needed both for building multi-modal tracking datasets and for benchmarking online tracking planners under repeatable conditions. We present Track A star (TA star), an offline search-based trajectory planner that targets the visibility-aware target tracking objective on a discretized four-dimensional spatio-temporal grid (x, y, z, t). TA star combines a layered Directed Acyclic Graph (DAG) search with three engineering optimizations: cross-time obstacle distance caching against a Bounding Volume Hierarchy (BVH), per-layer beam pruning, and a configurable multi-ray visibility evaluator. TA star employs a beam-pruned heuristic search on this discrete graph to efficiently find high-quality tracking trajectories. While it trades strict theoretical optimality for practical scalability, our empirical results demonstrate robust, near-baseline visibility performance at a fraction of the computational cost. On a 1000-scenario stress test across eight CARLA Optimized maps, TA star converges on all scenarios and completes in 45 s using 32 workers; on a 248-scenario controlled comparison against an unoptimized priority-queue A star baseline (BinaryHeap implementation) under identical scenario inputs and a 5 x 10^6 expansion cap, TA star reduces mean planning time by 23.0x and worst-case planning time by 11.8x, while raising convergence from 56.9% to 100%. On the n=141 baseline-converged subset, TA star changes average visibility by only -0.15 percentage points (pp), with no scenario exceeding a 5 pp drop. We position TA star as a practical offline reference planner under these specific conditions, with limitations and failure cases discussed for environments such as Town07 dense vegetation.