Objective non-stationarity measures are resource intensive and impose critical limitations for real-time processing solutions. In this paper, a novel Hard Label Criteria (HLC) algorithm is proposed to generate a global non-stationarity label for acoustic signals, enabling supervised learning strategies to be trained as stationarity estimators. The HLC is first evaluated on state-of-the-art general-purpose acoustic models, demonstrating that these models capture stationarity information. Furthermore, the first-of-its-kind HLC-based Network for Acoustic Non-Stationarity Assessment (NANSA) is proposed. NANSA models outperform competing approaches, achieving up to 99% classification accuracy, while solving the computational infeasibility of traditional objective measures.