First Nations peoples occupy one-quarter of the world's land area, safeguarding 80% of its biodiversity. Sustainable development frameworks acknowledge and include culture's role but fail to give it a special place, specifically First Nations peoples' (Indigenous) cultures. Hence, this study presents a sustainable development model that recognises their cultures—the underlying motivation is that adopting the United Nations Sustainable Development Goals (UN SDGs) as the 2030 Sustainability Agenda for these peoples' cultural capital development has posed two challenges. First, the goal-related targets and indicators are objectified, encouraging these to be attained as separate goals, but since First Nations cultures are based on relationships and interconnectedness, thinking linearly about these goals misaligns with these cultures. Second, these targets and indicators are not framed to provide special recognition and inclusion of these peoples' cultural knowledge as crucial for sustainable development. Therefore, this study uses the Gaia theory, the theory of distributive justice and the interaction theory of First Nations cultures to propose an empirically testable structural equation model for analysing empirical data using the UN SDGs as goal posts, towards advancing sustainable development. A model application is proposed for non-governmental organisations serving First Nations peoples. The integrated model shows the interrelationships between various types of capital, including these peoples' cultural capital, required for sustainable development.