The interaction between the membrane spike (S) protein of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and the transmembrane angiotensin-converting enzyme 2 (ACE2) receptor of the human epithelial host cell is the first step of infection, which has a critical role for viral pathogenesis of the current coronavirus disease-2019 (COVID-19) pandemic. Following the binding between S1 subunit and ACE2 receptor, different serine proteases, including TMPRSS2 and furin, trigger and participate in the fusion of the viral envelope with the host cell membrane. On the basis of the high virulence and pathogenicity of SARS-CoV-2, other receptors have been found involved for viral binding and invasiveness of host cells. This review comprehensively discusses the mechanisms underlying the binding of SARS-CoV2 to ACE2 and putative alternative receptors, and the role of potential co-receptors and proteases in the early stages of SARS-CoV-2 infection. Given the short therapeutic time window within which to act to avoid the devastating evolution of the disease, we focused on potential therapeutic treatments—selected mainly among repurposing drugs—able to counteract the invasive front of proteases and mild inflammatory conditions, in order to prevent severe infection. Using existing approved drugs has the advantage of rapidly proceeding to clinical trials, low cost and, consequently, immediate and worldwide availability.