We use femtosecond extreme-ultraviolet time- and angle-resolved photoelectron spectroscopy to study the ultrafast photo-induced suppression of the charge-density wave (CDW) in 1T-TiSe2. In the following non-equilibrium electron dynamics after femtosecond laser excitation, we see that hot-carrier multiplication is the primary driver for the ultrafast CDW suppression. As soon as the optically excited carriers have relaxed to a quasi-equilibrium hot Fermi-distribution electron gas, the CDW suppression stops. Theoretical calculations of the hot-carrier scattering processes and the screening properties further link the carrier multiplication to the observed CDW gap dynamics