To better understand how immunity develops against SARS-CoV-2 during the pandemic period of 2020 to 2022, we analyzed the immune response of a small group of university staff and students who were either infected or vaccinated. We investigated the levels of receptor-binding domain (RBD)-specific and nucleocapsid (N)-specific IgG and IgA antibodies in serum and saliva samples taken early (around 10 days after infection or vaccination) and later (around 1 month later), as well as N-specific T-cell responses. One patient who had been infected in 2020 developed serum RBD and N-specific IgG antibodies, but declined 8 months later, then mRNA vaccination in 2021 produced a higher level of anti-RBD IgG than natural infection. In the vaccination of naïve individuals, vaccines induced anti-RBD IgG, but it declined after 6 months. A third vaccination boosted the IgG level again, albeit to a lower level than after the second. In 2022, when the Omicron variant became dominant, familial transmission occurred even among vaccinated people. In infected individuals, the levels of serum anti-RBD IgG antibodies increased later, while anti-N IgG peaked earlier. The N-specific activated T cells expressing IFN- or CD107a were detected early. In saliva, SARS-CoV-2-specific IgG but not IgA was detected. Interestingly, two individuals showed a temporary peak in RBD- and N-specific IgA antibodies in their saliva on the second day after infection. Thus, SARS-CoV-2 infection triggers typical immune responses in humans against acute viral infections, but mucosal immune responses, which are temporarily induced early during infection, may be more important for protection than current intramuscular vaccines.