The collective response of matter is ubiquitous and widely exploited, e. g., in plasmonic, optical, and electronic devices. Here we trace on an attosecond time scale the birth of collective excitations in a finite system and find distinct features in this regime. Combining quantum chemical computation with quantum kinetic methods, we calculate the time-dependent light absorption and refraction in fullerene that serve as indicators for the emergence of collective modes. We explain the numerically calculated transient features by an analytical model and point out the relevance for ultrafast photonic and electronic applications. A scheme is proposed to measure the predicted effects via the emergent attosecond metrology.