This paper addresses the critical gap between engineering projects and the United Nations Sustainable Development Goals (UN SDGs), proposing an integrated socio-technical framework to develop human-centred solutions for complex social challenges. The framework bridges social and technical methodologies, ensuring that engineering solutions are technically robust and deeply rooted in human context. The methodology involves a seven-step process integrating social, technical, and human-centred design approaches. It includes research, stakeholder engagement, thematic analysis, corroboration with existing literature, design input development, weighted evaluation, and technical assessment. The framework’s effectiveness is demonstrated through a case study on homelessness in Australia. Results from the case study reveal the importance of holistic, integrated support services and aligning the needs of homeless individuals with Maslow’s Hierarchy of Needs. The study generated design inputs addressing various well-being aspects, from basic needs to self-actualisation opportunities. A weighted evaluation of these inputs highlighted the need for a balanced approach to addressing homelessness. The research contributes to efforts addressing the UN SDG of eliminating poverty by providing a structured approach to developing socially sustainable solutions. It emphasises the interconnectedness of social and technical disciplines in addressing complex social challenges. Recommendations include further evaluation of the framework, expanded research on homelessness, cohort analysis, model evaluation, technical feasibility assessments, longitudinal studies, and fostering interdisciplinary collaborations. This paper presents a novel approach to humanitarian engineering that promises more effective, sustainable, and socially impactful solutions to global challenges.