Background: After the onset of the COVID-19 pandemic, social restriction measures were implemented, among them, the adaptation of university teaching to online modality until the end of the 2019–2020 school year in order to stop the spread of the SARS-CoV-2 virus. At the beginning of the 2020–2021 school year, the Spanish universities opted for face-to-face teaching. To that end, different special measures and adaptations were implemented in higher education facilities, aimed at minimizing the risk of infection and ensuring safe face-to-face learning. The objective was to explore and describe the level of fear of first-year students after the start of in-person classes in the context of the COVID-19 pandemic. Methods: The sample was 185 first-year students who were evaluated on the first day of class. For that purpose, an ad-hoc questionnaire was administered to collect demographic information and to find the level of fear and concern. The Fear of COVID-19 Scale was used to assess the severity of the participants’ fear of the pandemic situation. Results: The results indicate that participating university population does not report fear of the virus, but they describe various psychosomatic characteristics, such as increased pulse rate and heart palpitations (p = 0.008) and insomnia (p = 0.05) when they think about infection with coronavirus. Nevertheless, when data are disaggregated by gender, we observe differences specifically in women (83.2%), such as fear (p = 0.006) and sweaty hands when they think of the virus (p = 0.023). Conclusions: Incoming university freshmen do not express concern or fear of potential infection with COVID-19, but they are concerned about family transmission after beginning face-to-face classes.