Due to the COVID-19 pandemic, and pursuant to the governments' order of citizens remaining at home, several countries were required to transition from face-to-face instruction to an online model to provide higher education to their students . While factors affecting the use of online learning are diverse and have been studied by models of use and acceptance of technology, this cross-sectional study explores the factors unique to the current emergency situation that influence students' use and acceptance of emergency online learning . Moreover, it proposes a model to predict a student's cognitive engagement in Mexico, Peru, Turkey, and the USA . This is a quantitative study with an exploratory and descriptive scope and cross-sectional design . Data was collected from 1009 students from the four countries, who completed surveys anonymously . The factors analyzed were attitude, affect, and motivation, perceived behavioral control (ease of use, self-efficacy, and accessibility), and cognitive engagement . The data was analyzed using descriptive, correlation, and regression analysis . The predictive model shows that students' attitude toward online learning impacts their cognitive engagement in Mexico, Peru, and the USA . Furthermore, self-efficacy is a significant moderator for cognitive engagement in all four countries . The model also shows that each country has different determinants for cognitive engagement . Understanding the factors that affect the use of emergency online learning is essential for the success and/or achievement of its maximum benefits in situations like a global pandemic . Limitations of this study have been identified as use of convenience sampling, and an inability to explore factors related to instruction and system attributes . Professors who did not teach online learning lacked knowledge about online educational strategies and used the technological resources that were immediately available to them . Therefore, research that explores the use of instructional strategies and the use of technological systems during emergency online learning is necessary . This study includes suggestions to incorporate open educational resources that use microlearning and emphasizes the importance of student self-efficacy; because it was predictor of cognitive engagement in all four countries . Faculty and higher education institutions can and should develop strategies to increase students' sense of self-efficacy.