Asymmetric quantum well systems are excellent candidates to realize semiconductor light emitters at far-infrared wavelengths not covered by other gain media. Group-IV semiconductor heterostructures can be grown on silicon substrates and their dipole-active intersubband transitions could be used to generate light from devices integrated with silicon electronic circuits. Here, we have realized an optically pumped emitter structure based on a three-level Ge/Si0.18Ge0.82 asymmetric coupled quantum well design. Optical pumping was performed with a tunable free-electron laser emitting at photon energies of 25 and 41 meV, corresponding to the energies of the first two intersubband transitions 0→1 and 0→2 as measured by Fourier-transform spectroscopy. We have studied with a synchronized terahertz time-domain spectroscopy probe the relaxation dynamics after pumping, and we have interpreted the resulting relaxation times (in the range 60 to 110 ps) in the framework of an out-of-equilibrium model of the intersubband electron-phonon dynamics. The spectral changes in the probe pulse transmitted at pump-probe coincidence were monitored in the range 0.7-2.9 THz for different samples and pump intensity and showed indication of both free carrier absorption increase and bleaching of the 1→2 transition. The quantification from data and models of the free carrier losses and of the bleaching efficiency allowed us to predict the conditions for population inversion and to determine a threshold pump power density for lasing around 500 kW/cm2 in our device. The ensemble of our results shows that optical pumping of germanium quantum wells is a promising route towards silicon-integrated far-infrared emitters.