PROJECT STELLA GENESIS: Relativistic Interstellar Travel Within a Single Human Lifespan presents a comprehensive hypothesis demonstrating that crewed interstellar travel to distant galaxies (Andromeda Galaxy, 2.5 million light-years) is physically possible, engineering-feasible, and economically justified within 125 years. This work combines two proven physics principles—relativistic time dilation at near-light velocities (0.90-0.95c) and nuclear fusion propulsion—to compress multi-million-year Earth-frame journeys into hundreds of thousands of subjective years for crews. The hypothesis establishes fusion rocket superiority over alternatives through detailed energy budget calculations, proposes a realistic three-phase deployment timeline (2026-2150) with estimated costs of $7-16 trillion (0.05-0.1% global GDP), and comprehensively addresses critical engineering systems including miniaturized fusion reactors (490 GW continuous power), thermal management (140,000 km² radiators), radiation shielding, long-duration life support, and autonomous navigation. Rather than invoking breakthrough physics or exotic technologies, all systems are grounded in established physics, demonstrated engineering, and near-term technological development. This work bridges current spaceflight capabilities and speculative science fiction by rigorously demonstrating that interstellar human exploration, while extraordinarily difficult, is neither impossible nor implausible. The hypothesis encompasses sections on relativistic physics foundations, current propulsion limitations, fusion propulsion advantages, detailed energy budgets, technical requirements, realistic deployment timelines, engineering challenges, and comparative analysis against alternative propulsion concepts. Target audiences include aerospace engineers, astrophysicists, space mission planners, physicists, and futurists interested in long-term human space exploration beyond the solar system.