A novel methodology is developed to dynamically assess the energy and material investments required over time to achieve the transition from fossil fuels to renewable energy sources in the electricity sector. The obtained results indicate that a fast transition achieving a 100% renewable electric system globally by 2060 consistent with the Green Growth narrative could decrease the EROI of the energy system from current similar to 12:1 to similar to 3:1 by the mid-century, stabilizing thereafter at similar to 5:1. These EROI levels are well below the thresholds identified in the literature required to sustain industrial complex societies. Moreover, this transition could drive a substantial rematerialization of the economy, exacerbating risk availability in the future for some minerals. Hence, the results obtained put into question the consistence and viability of the Green Growth narrative.