India's demographic dividend discourse has systematically overlooked the "sandwich generation" crisis—middle-aged individuals (40-60) trapped between youth-centric employment policies and elderly-focused welfare schemes. This paper introduces the Bharat Reboot Fund (BRF), a pioneering socio-economic intervention based on the novel Progressive Equity Transfer Model (PETM). Unlike traditional incubators requiring pre-existing capital, the BRF operates through a reverse equity dilution mechanism where the state initially holds majority ownership in micro-enterprises and progressively transfers equity to entrepreneurs based on performance milestones. This addresses three critical gaps: the "missing middle" in social security architecture, the temporal mismatch between entrepreneurial aspirations and capital availability, and the absence of dignity-preserving reintegration mechanisms. A mixed-methods study including a pilot (n=100) across Mumbai, Bangalore, and Chennai demonstrates 75% business survival rates versus 50% in traditional microfinance controls, with significant psychological empowerment gains. Econometric and game-theoretic models validate the PETM's feasibility, while longitudinal case studies highlight scalability potential. The BRF represents a paradigmatic shift from welfare dependency to asset-building entrepreneurship, offering a replicable framework for emerging economies addressing structural unemployment.