The ultrafast transition of an optical phonon resonance to a coupled phonon-plasmon system is studied. After 10-fs photoexcitation of i-InP, the buildup of coherent beats of the emerging hybrid modes is directly monitored via ultrabroadband THz spectroscopy. The anticrossing is mapped out as a function of time and density. A quantum kinetic theory of microscopic carrier-carrier and carrier-LO-phonon interactions explains the delayed formation of the collective modes. The buildup time is quantitatively reproduced to scale with the oscillation cycle of the upper branch of the coupled resonance.