Efficient exploration and mapping in unknown indoor environments is a fundamental challenge, with high stakes in time-critical settings. In current systems, robot perception remains confined to line-of-sight; occluded regions remain unknown until physically traversed, leading to inefficient exploration when layouts deviate from prior assumptions. In this work, we bring non-line-of-sight (NLOS) sensing to robotic exploration. We leverage single-photon LiDARs, which capture time-of-flight histograms that encode the presence of hidden objects - allowing robots to look around blind corners. Recent single-photon LiDARs have become practical and portable, enabling deployment beyond controlled lab settings. Prior NLOS works target 3D reconstruction in static, lab-based scenarios, and initial efforts toward NLOS-aided navigation consider simplified geometries. We introduce SuperEx, a framework that integrates NLOS sensing directly into the mapping-exploration loop. SuperEx augments global map prediction with beyond-line-of-sight cues by (i) carving empty NLOS regions from timing histograms and (ii) reconstructing occupied structure via a two-step physics-based and data-driven approach that leverages structural regularities. Evaluations on complex simulated maps and the real-world KTH Floorplan dataset show a 12% gain in mapping accuracy under < 30% coverage and improved exploration efficiency compared to line-of-sight baselines, opening a path to reliable mapping beyond direct visibility.