Higher education is a powerful tool for migrant integration into destination countries. This paper presents an empirical comparison between native and migrant students in Chile, focusing on their trajectory through different transitions: high school graduation, performance on university entrance exams, and decision to enroll in technical or university higher education. Results show that, when controlling for school performance, natives are more likely to complete every transition compared to migrant students, except in the enrollment to technical higher education where migrants have a higher rate. However, we also show that the timing of arrival to the educational system matters and that the differences between groups completely disappear if migrant students arrive before age 10 in the educational system. Therefore, we expand the educational literature by empirically showing that "when" migrants enter the school system is crucial. If they arrive early in life, they can have a trajectory similar to that of native students.