Abstract: The rapid proliferation of electromagnetic (EM) pollution necessitates the urgent development of high-performance microwave absorption (MA) materials with ultra-broadband capabilities. However, conventional trial-and-error design paradigms are constrained by the path-dependent nature of the fabrication process, where the specific impregnation history strictly governs the final gradient distribution and impedance matching. To address this, this study proposes a sequence-aware inverse design framework that integrates a Long Short-Term Memory (LSTM) neural network with a Genetic Algorithm (GA). Leveraging a process-property database derived from multi-step impregnated polyurethane/carbon nanotube (PU/CNT) foams, a high-fidelity LSTM surrogate model is developed to decode the complex temporal dependencies within the impregnation history and accurately predict frequency-dependent complex permittivity. Subsequently, the GA utilizes this predictive model to navigate the design space, identifying an optimal impregnation pathway that yields a precise three-layer gradient configuration. The resulting optimized foam, characterized by a rational stepwise increase in dielectric loss, achieves an exceptional average reflection loss (RL) of −24.2 dB and an ultra-wide effective absorption bandwidth (EAB) covering the full 2–18 GHz range. This work demonstrates the efficacy of history-based data-driven strategies in accelerating material discovery, offering a scalable paradigm for the intelligent design of advanced functional composites.