This work introduces the key aspects to optimize binder-based microstructures using machine learning techniques, with the primary goal of enhancing their uptake properties, particularly the capacity to absorb carbon dioxide (CO2). The utilization of CO2 in concrete and its components is currently achieved by converting gaseous CO2 into solids (carbonates) through a process known as mineral carbonation. To bind CO2 in solids as carbonates, two essential components are required: i) a supply of cations to form solid carbonate minerals, and ii) a supply of alkalinity that enables the rapid conversion of CO2 into carbonate ions. The most common carbonate formed is calcium carbonate (CaCO3), where calcium serves as the cation. Alternatively, systems rich in magnesia also show potential for CO2 curing, resulting in the formation of hydroxy-magnesites and/or other magnesium-carbonate hydrates. The proposed approach encompasses several key numerical steps to design a micro-structured concrete absorber based on machine-learning procedures, such as data collection and model training, rendering microstructural variables compatible with machine-learning algorithms, selection of appropriate machine-learning algorithms, model validation, optimization, and prediction. By enabling the exploration of a vast range of microstructures and mineral carbonation processes, this approach offers an avenue to engineer concrete materials with superior CO2 absorption capacities, contributing to the creation of sustainable and environmentally friendly construction materials. The synergy between machine learning and concrete science has the potential to revolutionize the construction industry's approach to enhancing properties while minimizing environmental impact.