The design of advanced engineering materials increasingly requires navigating high-dimensional design spaces under competing performance and sustainability objectives. In this contribution, we position multi-objective quantum optimization as an emerging computational tool for data-driven materials design, with a particular focus on constrained, multi-objective and non-convex optimization problems \cite{Plehn2025}. Building on recent progress in data-driven QUBO-based optimization, we present an active learning framework that combines factorization machine surrogate models with QUBO optimization (FM+QO). Two methodological advances are introduced. First, a constraint-guided feature mapping (CGFM) strategy eliminates systemic equality constraints by construction through a data-driven coordinate transformation, significantly simplifying QUBO formulations and accelerating optimization. Second, a data-driven Tchebycheff scalarization (DDTS) approach enables efficient multi-objective optimization and robust exploration of non-convex Pareto fronts within the QUBO formalism. The methods are demonstrated on a multi-phase aluminum alloy design problem at the microstructural level, considering competing thermal and mechanical objectives. The results show substantial improvements in optimization efficiency, Pareto front quality, and solution diversity compared to standard weighted-sum QUBO scalarization approaches, establishing CGFM and DDTS as practical algorithmic building blocks for data-driven quantum optimization workflows. Beyond the validated model problem, we discuss ongoing work that applies the presented FM+QO framework to sustainability-driven alloy design, with a focus on recycling mixed scrap aluminum streams for aerospace applications. Here, scrap feedstock compositions are combined using CALPHAD-based thermodynamic and property models to evaluate resulting thermal and mechanical performance. First results obtained on quantum annealing hardware will be presented and critically assessed in the context of near-term quantum optimization for sustainable materials engineering. Overall, this contribution bridges computational mechanics, machine learning, and quantum optimization, and outlines a pathway toward integrating QUBO-based methods into next-generation, sustainability-aware materials design pipelines.