We describe how we redesigned, because of the 2020 COVID-19 pandemic, the CS1 course for Math undergraduates to be held online yet reflecting the face-to-face (F2F) experience as much as possible. We present the course structure, the IT tools we used, and the strategies we implemented to preserve the benefits of a synchronous experience. We discuss the positive and negative aspects that emerged from the students' opinion qualitative analysis. We use the COI framework as a lens to explain what worked, what did not, and what can be improved to strengthen the perception of a F2F experience and mitigate the "presence paradox" we found: despite students being enthusiastic about the online format, most would still prefer a F2F course.