<p>Sustainability-driven inventory model has emerged as an essential research area in the age of environmental restrictions and initiatives from the government. This study proposes an innovative probabilistic inventory model that integrates preservation technology, government-subsidized green innovation technologies, carbon-emission reduction policies, and advertising-induced demand uncertainty addressing the economic, environmental, and social sustainability challenges simultaneously. The approach includes government subsidies designed to encourage green innovation and sustainable corporate practices. Unlike conventional models, the proposed framework includes stochastic demand that is endogenously influenced by inventory level, advertising frequency, and product greenness, as well as explicit incorporation of government subsidies as a decision-dependent incentive for emission reduction and green investment. While degradation is non-instantaneous and is controlled from the initial stage through preservation and the carbon emissions are regulated through a tax mechanism. The model formulates a novel nonlinear profit-maximization objective that determines optimal advertising frequency, greenness level, and initial inventory under probabilistic demand and environmental constraints in a unified framework. Hybrid Particle Swarm Optimization-Genetic Algorithm (PSO-GA) is employed as a reliable metaheuristic method to obtain optimal solutions in order to handle the high nonlinearity, stochastic structure of the problem and the computational complexity of the model. Numerical experiments and sensitivity analyses demonstrate that government subsidies significantly enhance sustainable demand fulfilment, reduce carbon emissions, and improve overall profitability. The findings provide actionable insights for policymakers and managerial professionals by quantifying the trade-offs between environmental regulations, subsidy policies, and operational decisions in sustainable inventory systems.</p>