Autonomous exploration in unknown environments is a critical challenge in robotics, particularly for applications such as indoor navigation, search and rescue, and service robotics. Traditional exploration strategies, such as frontier-based methods, often struggle to efficiently utilize prior knowledge of structural regularities in indoor spaces. To address this limitation, we propose Mapping at First Sense, a lightweight neural network-based approach that predicts unobserved areas in local maps, thereby enhancing exploration efficiency. The core of our method, SenseMapNet, integrates convolutional and transformerbased architectures to infer occluded regions while maintaining computational efficiency for real-time deployment on resourceconstrained robots. Additionally, we introduce SenseMapDataset, a curated dataset constructed from KTH and HouseExpo environments, which facilitates training and evaluation of neural models for indoor exploration. Experimental results demonstrate that SenseMapNet achieves an SSIM (structural similarity) of 0.78, LPIPS (perceptual quality) of 0.68, and an FID (feature distribution alignment) of 239.79, outperforming conventional methods in map reconstruction quality. Compared to traditional frontier-based exploration, our method reduces exploration time by 46.5% (from 2335.56s to 1248.68s) while maintaining a high coverage rate (88%) and achieving a reconstruction accuracy of 88%. The proposed method represents a promising step toward efficient, learning-driven robotic exploration in structured environments.