Air pollution is a leading global health threat, yet many developing countries lack the dense monitoring infrastructure needed for accurate exposure assessment and informed policy. Optimal Sensor Placement (OSP) is a foundational challenge in expanding monitoring capacity. While mutual information (MI) offers a principled criterion for selecting informative sensor locations, its computational cost grows with both the number of placements and the density of the candidate grid. We present a scalable, continuous optimization framework that treats sensor coordinates as differentiable parameters and directly maximizes MI. Unlike standard approaches, our method is computationally efficient—its runtime is independent of both the number of placements and the size of the search grid—making MI-based acquisition feasible over large spatial domains. On a continental-scale PM$_{2.5}$ dataset, our method outperforms random placement and the widely-used Maximum Predictive Variance heuristic. In a focused regional study, it approaches the performance of greedy MI while being orders of magnitude faster. Our framework enables practical, information-theoretic sensor placement for real-world environmental monitoring.