The dynamic development of e-learning technologies caused by the global epidemiological situation during the last year has prompted the rapid adaptation of the education sector to new challenges. At the same time, many barriers and challenges have emerged, especially at the initial period of e-learning implementation. The identification of factors determining the adoption of e-learning should be the source of information needed to improve the methods and tools used by educational institutions. In the era of strong competition, higher education institutions need to improve their business models or build new ones e.g. based on remote learning. The article aims to identify the essential success factors and their interlinks that explain the initial stages of adoption of an e-learning system by university students in Poland. The author built three regression models which explain relationships between six input variables, i.e., the perceived usefulness (PU), the perceived ease of use (PEU), facilitating conditions (FC), computer self-efficacy (CSE), the preparedness level (PL), and previous experience (PE); and three output variables, i.e., satisfaction and personal development (SPD), attitude toward e-learning (AT), and intention to use (IU). The variable “satisfaction and personal development” (SPD) was newly added to the model. Data was collected with the help of a survey, which was conducted using the CAWI (computer-assisted web interview) technique. In total, 982 completed questionnaires were received. Results achieved using a regression analysis confirmed that the perceived usefulness played a crucial role in building the attitude of students toward e-learning and achieving satisfaction and personal development of the users. Only in the case of two analyzed variables, the obtained results confirmed statistically significant differentiation within the two gender groups. Results confirmed that men had declared a high level of computer self-efficacy. The variable “facilitating conditions” received higher marks from women. The research carried out and the results obtained may form the basis for building strategies for the development of universities and building business models in which e-learning plays an important role.