This paper introduces a visionary approach to sustainable software engineering through the lens of genetic improvement (GI). We propose leveraging GI techniques to automatically optimize software architectures for sustainability, focusing on reducing energy consumption without compromising performance. By integrating GI with architectural design processes, we envision a future where software systems evolve towards optimal sustainability through continuous, automated refinements. Our approach not only aims to enhance the greenness of software, but also to pioneer a shift in architectural practices, paving the way for a new era of environmentally conscious software development.