We perform ultrafast pump-probe experiments on a 50 period Ge/SiGe multiple-quantum-well structure held at room temperature. Tunable 80 fs pulses emitted by an opto-parametric amplifier are used as a pump and a white-light supercontinuum generated directly from a 1 kHz Ti:sapphire regenerative amplifier system is used as a probe. The resulting spectro-temporal response shows three distinct temporal regimes. Coherent oscillations dominate at negative times yielding a well-defined time zero across the whole detected spectral range. Dynamics are observed within the direct conduction band valley during and shortly after the excitation while the electrons are also scattered towards the indirect minima. After several hundreds of fs to a few ps almost all electrons populate the L-valley states. These carriers decay out of the L-valleys on a timescale longer than several ns. During the first ps, carrier inversion is obtained for strong enough pumping due to faster intra-valley than intervalley scattering. The obtained gain values are similar in magnitude to those observed in typical III-V compound semiconductors.