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We investigate the generation of entanglement between two quantum emitters through the inverse-design engineering of their photonic environment. By means of a topology-optimization approach acting at the level of the electromagnetic Dyadic Green's function, we generate dielectric cloaks operating at different inter-emitter distances and incoherent pumping strengths. We show that the structures obtained maximize the dissipative coupling between the emitters under extremely different Purcell factor conditions, and yield steady-state concurrence values much larger than those attainable in free space. Finally, we benchmark our design strategy by proving that the entanglement enabled by our devices approaches the limit of maximum-entangled-mixed-states.