We investigate the generation and real-time monitoring of coherent vibrational wave packets in the electronic ground state of supersonic jet-cooled potassium dimers. Vibrationally excited wave packets with mean quantum numbers <(nu)over bar> = 6 and <(nu)over bar> = 11 are generated by a stimulated Raman process which is enhanced by an electronic resonance. Two ultrashort laser pulses of different wavelengths induce the pump and the dump process. The population of the final hot ground-state wave packets is successfully controlled by a variable time delay between the pump and the dump process, which enables us to wait with the dumping for the optimal Franck-Condon overlap between the intermediate and the predicted final vibrational wave packet in the electronic ground state.