In detailed Earth models that require extensive computation time, it is difficult to make an a priori prediction of the possibility of multistationarity. The potential for multistationarity, or the existence of steady-state multiplicity, in the Earth System raises concerns that the planet could reach a climatic `tipping point', rapidly transitioning to a warmer steady-state from which recovery may be practically unattainable. In this study, we demonstrate Chemical Reaction Network Theory (CRNT) analysis of a simple heuristic box model of the Earth System carbon cycle with the human intervention of Direct Air Capture. CRNT leverages parameter-minimal analysis, relying primarily on the graphical and kinetic structure of the reaction network system, to identify necessary conditions for steady-state multiplicity. The analysis reveals necessary conditions for the combination of system parameters where steady-state multiplicity may exist. Moreover, the analysis provides insights into key system properties, such as absolute concentration robustness and some conditions for atmospheric carbon reduction.