This article presents the research results in relation to an interdisciplinary teaching innovation project—Teaching and Learning of Social Sciences and Teaching and Learning of Natural Sciences—with Early Childhood Preservice Teachers (ECPT) at the University of Alcalá (Spain) in the pandemic context by COVID-19 during 2020–2021 (N = 55): 52 women (94.55%) and 3 men (5.45%) from 20 to 22 years of age. The main research problem is to know if the ECPT improves the learning to learn competence after a challenge-based learning (CBL) linked to virtual tour in a museum. The main objective was to improve the learning to learn competence, during a virtual tour at the Community of Madrid Regional Archaeological Museum (MAR) (Alcalá de Henares, Spain) for a reflective training of students to understand problems of the past and present and future global challenges, promote collaborative and multidisciplinary work, and defend ethics and leadership. In order to ascertain the level of acquisition of this competence in those teachers who were being trained, their self-perception—pretest–posttest—of the experience was assessed through a system of categories adapted from the European Commission. ECPT worked, in small groups and using e/m-learning tools, ten challenges and one storytelling cooperatively with university teachers to solve prehistoric questions related to current situations and problems. Subsequently, two Early Childhood Education teachers from a school in Alcalá de Henares reviewed the proposals and adapted them for application in the classroom of 5-year-old boys and girls. The results show an improvement in this competence in Early Childhood Preservice Teachers: total score pre-post comparison paired-samples Wilcoxon test result shows a statistically significant difference (p > 0.001); an evaluation rubric verified the results of self-perception. Second, we highlight the importance of carrying out virtual museum tours from a challenge-based learning for the development of big ideas, essential questions, challenges, and activities on socioeconomic, environmental, and emotional knowledge, skills, and attitudes. Third, this experience shows the insufficient educational adaptation of the virtual museum tour to the Early Childhood Education stage from a technological and didactic workshops point of view, but there is a diversity of paleontological and archaeological materials and a significant sociocritical discourse.