The COVID-19 pandemic severely upended cultural and creative production, consumption, and interactions in cities. Open green spaces, parks, forests, and gardens—green infrastructure—were instead utilized by citizens as a substitute for stimulating social interactions, sustainable tourism, and green growth. (1) The purpose of this research is to understand whether the availability of green infrastructure relates to the Cultural and Creative Cities Monitor (CCCM) benchmarking project developed by the Joint Research Centre of the European Commission performance. Does new evidence suggest revising the CCCM conceptual framework and related urban policies, especially in relation to the EU Green Deal? (2) Data from OpenStreetMap was used to count the amount of green infrastructure in 184 European Cities covered by the CCM and was then correlated with the sub-indices of the CCCM. (3) We found a moderately positive correlation of green infrastructure with the cultural vibrancy of a city and a weak positive correlation with the enabling environment of a city. (4) In light of the COVID-19 pandemic, the EU Green Deal and several other policy initiatives aimed at urban greening, we recommend that the CCCM include an Urban Nature sub-index as one of the performance indicators of the CCCM. An Urban Nature sub-index will broaden the goal of the CCCM by providing policymakers with a better understanding of actions and strategies to allow culture to contribute to social inclusion and green growth strategies in cities.