In this period of extreme changes in our society, issues related to the health and well-being of citizens are considered essential for the future of a united and prosperous Europe. Achieving the Sustainable Development Goals (SDGs) at EU level by 2030 requires hard work done in a transformative way in order to implement a set of coherent, evidence-informed policies that address health, well-being and all their determinants throughout the course of life and across all sectors of government and society. The objective of this paper is to assess the stage of fulfillment of all SDG targets in relation to health and well-being at EU level, based on the current trend of each indicator, for each EU member country. Based on the Eurostat SDG data set for 2007–2018, the individual trends were forecast using the AAA (Holt-Winters) version of the exponential smoothing (ETS) algorithm. The research results are surprising, on the one hand showing the possibility that some targets will be reached, but also indicating that a large percentage of targets will not be reached if the current trend is continued, especially due to disruptive change generated by the current pandemic. There is a need to increase the involvement of all member states, but also ensure a deeper involvement at the level of EU institutions, to provide full support for meeting the targets proposed by the 2030 Agenda, ensuring prosperity and health for all European citizens, and becoming a model for all the states of the world.