This paper conducts a detailed quantitative study of the indicated long-term levels, nature and dynamics of sustainability at the global spatial scale over time, within the context of the vulnerability of the environment-human relationship and system. In this study, the Sustainability Dynamics Framework is applied to the results of the Notre Dame Global Adaptation Initiative index for the period 1995–2018. The study indicates that the obtained S-values at the global spatial scale throughout the specified period were consistent with very weak unsustainability occurring. Through statistical analysis, the study indicates that the triumvirate of influencing factors (Population, GDP, Greenhouse Gases) have a significant influence and impact individually and cumulatively upon obtained S-values. The study then determines the net change in obtained E, HNI and S-values, and consequently evaluates the dynamics of the rate of change of the Earth System ( dE/dt), as defined in the Anthropocene Equation theory. To support this, Fourier analysis of net change of S-values is applied for the first time within the SDF application methodology, using eight time periods of 16 years’ duration over the period 1996–2018. The analysis indicates continuous overlapping cycles of 7 years’ duration, consisting of a lag time of 3 years leading to an impact period of 4 years. The Fourier analysis potentially indicates clearly for the first-time humanity’s footprint signal upon the environment-human relationship and system in the Anthropocene. The study concludes that humanity’s actions and inactions have resulted in the indicated unsustainability and vulnerability of the environment-human relationship and system. As a consequence, there is a potential realistic risk of systemic collapse unless fundamental changes occur in respect to the global environment-human relationship.