More than two years on, the COVID-19 pandemic continues to wreak havoc around the world and has battle-tested the pandemic-situation responses of all major global governments. Two key areas of investigation that are still unclear are: the molecular mechanisms that lead to heterogenic patient outcomes, and the causes of Post COVID condition (AKA Long-COVID). In this paper, we introduce the HYGIEIA project, designed to respond to the enormous challenges of the COVID-19 pandemic through a multi-omic approach supported by network medicine. It is hoped that in addition to investigating COVID-19, the logistics deployed within this project will be applicable to other infectious agents, pandemic-type situations, and also other complex, non-infectious diseases. Here, we first look at previous research into COVID-19 in the context of the proteome, metabolome, transcriptome, microbiome, host genome, and viral genome. We then discuss a proposed methodology for a large-scale multi-omic longitudinal study to investigate the aforementioned biological strata through high-throughput sequencing (HTS) and mass-spectrometry (MS) technologies. Lastly, we discuss how a network medicine approach can be used to analyze the data and make meaningful discoveries, with the final aim being the translation of these discoveries into the clinics to improve patient care.