The European Union and several countries/regions classified the rare-earth elements (REEs), such as lanthanum, cerium, neodymium, and scandium, as critical due to the risk of supply interruption. For this reason, the growing demand for REEs has resulted in forgotten reserves receiving economic interest. So, the search for new sources and the development of chemical process is important, such as silicate-based ore. Since there is almost no literature on the extraction of REEs from this source, a new approach was developed in the present study. Direct leaching and acid baking were studied using sulfuric acid. The effect of the acid concentration, temperature, solid-liquid ratio, oxidizing/reducing medium, and acid dosage were studied. Results showed that the extraction of REEs achieved up to 80% at 90 °C in oxidizing medium, and scandium and iron achieved 13.5% and 65.0%, respectively. For the acid baking experiments, the results were better than direct leaching for REEs at over 85%. The scandium leaching rate was lower than direct leaching. On the other hand, the extraction of iron was lower in acid baking than direct leaching. The iron and scandium extraction rates were higher in lower temperatures (<200 °C) and acid dosages, achieving 50% and 6.3%, respectively. Future studies should explore thermal treatment before acid leaching.