The growth of Brazilian scientific production in recent years is remarkable, which motivates an investigation on the factors, inside and outside the country, that helped shape this wealthy research environment. This article provides a thorough analysis of the education of researchers that constitute the main Brazilian research groups, using data on about 6,000 researchers involved in the country's National Institutes of Science and Technology (INCT) initiative. Data on the steps taken by each researcher in her education, from the bachelor's degree to doctorate, including a possible postdoctoral experience, and employment, are extracted from an official curriculum vitae repository. The location and the time at which each career step occurred define spatiotemporal career trajectories. We then analyze such trajectories considering additional data, including the area of knowledge of the INCTs to which each researcher is associated. We found an increasing prevalence of Brazilian institutions in the education of Brazilian scientists, as the number of doctorates earned abroad is decreasing over time. Postdoctoral stages, on the other hand, often take place in Europe or in the United States. Taking an international postdoctoral position after a full education in Brazil suggests a drive towards seeking higher-level exchange and cooperation with foreign groups in a more advanced career stage. Results also show that Brazilian researchers tend to seek employment in regions that are close to the institutions at which they received their bachelor's degrees, suggesting low mobility within the country. This study can be instrumental in defining public policies for correcting distortions, and can help other developing countries that aim to improve their national science systems.