In the context of the circular economy and the adoption of one of its business models, namely ”resource recovery”, this study presents an opportunity to valorize industrial and urban wastes using alkaline activation technology to produce hybrid binders. Several alkali-activated binders were produced using response surface methodology based on a mixture of 45/45/10 clay brick waste, fly ash, and Portland cement. The compressive strength and setting time of each were evaluated. The hybrid cementitious pastes achieved up to 45 MPa after 28 days of setting. Based on the experimental data, two binders were selected as the cementitious matrix for composites, with paper sludge as the lightweight aggregate. Incorporating up to 45% volume of paper sludge allowed extrusion of the materials. The addition of paper sludge reduced the compressive and flexural strength. These results were explained by the decrease in density and the increase in porosity. However, there was an improvement in the thermal properties of the composites; in particular, the thermal conductivity range between 0.35 and 0.49 W/mK. Finally, it was found that the composites with 25% volume of paper sludge had the best combination of properties, positioning them as potential construction materials.