Fast and robust entanglement generation is a central requirement for scalable quantum technologies, where limited coherence time, parameter drift, and timing uncertainty can otherwise erase quantum advantage. We investigate entanglement generation in topological open quantum systems governed by an effective non-Hermitian Hamiltonian. For a lossy two-qubit dimer with asymmetric dissipation, tuning the coherent coupling across an exceptional point (EP) produces a PT-like crossover between decay-rate splitting and frequency splitting, which directly reshapes the conditional (no-jump) concurrence dynamics in the single-excitation manifold. Embedding the dimer into a non-Hermitian Su-Schrieffer-Heeger (SSH)-like ladder yields multiple EPs through edge-bulk hybridization. Our key contribution is a practical design rule: among these EPs, the operational one for entanglement is the “edge-mode EP,” defined by the EP whose coalesced eigenvector is maximally localized on the target edge pair; the near-optimal working point lies slightly above this EP, balancing preparation speed, no-jump success probability, timing-jitter tolerance, and robustness to bulk detuning disorder. Using thresholded operational metrics (preparation time, success probability, rate, jitter window, and disorder sensitivity), we map these trade-offs and show that topology-assisted confinement plus EP-enabled mode selection enables fast and robust heralded edge entanglement.