In the earliest phases of their evolution, stars gain mass through the acquisition of matter from their birth clouds. The widely accepted classical concept of early stellar evolution neglects the details of this accretion phase and assumes the formation of stars with large initial radii that contract gravitationally. In this picture, the common idea is that once the stars begin their fusion processes, they have forgotten their past. By analysing stellar oscillations in recently born stars, we show that the accretion history leaves a potentially detectable imprint on the stars’ interior structures. Currently available data from space would allow discriminating between these more realistic accretion scenarios and the classical early stellar evolution models. This opens a window to investigate the interior structures of young pulsating stars that will also be of relevance for related fields, such as stellar oscillations in general and exoplanet studies.