The aim of the article is to identify the main features of the approach of historical thought of the sixteenth century, first and foremost that of Spain, to the question of the origin of the indigenous peoples of the Americas. In general, this problem remains poorly studied in recent historiography (with the exception of the works of Lee Huddleston and Vladimir Acosta), although it is associated with one of the most important aspects of European understanding of the reality of the New World, not yet known to them, whether it be ethnic, spatial, historical. The main task of the author is to try to explain the fact that the study of the origin of the Indians, despite the abundance of various theories (Phoenician, Carthaginian, Hebrew, Ophirian, etc.), remained on the periphery of interest of European writers and thinkers throughout the sixteenth century. To answer this question, the author analyses the writings of some Renaissance writers (Fernando Colón, Cabello Balboa, José de Acosta, Gregorio García) who addressed this issue in order to identify the methods and ways of argumentation that they used in this case. The most popular of them, as shown in the article, were the analysis of the content of historical sources based on common sense, and the method of cultural and anthropological comparison of present inhabitants of the New World with ancient and modern peoples of the Old One. The article concludes that the European historical thought of the Renaissance eventually recognized its inability to answer the question of the origin of the Indians due to the extreme scarcity of historical data at its disposal and the irrelevance of the tools of historical analysis that it had.