Given the performance and efficiency optimizations realized by the computer systems and architecture community over the last decades, the dominating source of computing's carbon footprint is shifting from operational emissions to embodied emissions. These embodied emissions owe to hardware manufacturing and infrastructure-related activities. Despite the rising embodied emissions, there is a distinct lack of architectural modeling tools to quantify and optimize the end-to-end carbon footprint of computing. This work proposes ACT, an architectural carbon footprint modeling framework, to enable carbon characterization and sustainability-driven early design space exploration. Using ACT we demonstrate optimizing hardware for carbon yields distinct solutions compared to optimizing for performance and efficiency. We construct use cases, based on the three tenets of sustainable design---Reduce, Reuse, Recycle---to highlight future methods that enable strong performance and efficiency scaling in an environmentally sustainable manner.