Nonequilibrium pump-probe time domain spectroscopies can become an important tool to disentangle degrees of freedom whose coupling leads to broad structures in the frequency domain. Here, using the time-resolved solution of a model photoexcited electron-phonon system we show that the relaxational dynamics are directly governed by the equilibrium self-energy so that the phonon frequency sets a window for slow versus fast recovery. The overall temporal structure of this relaxation spectroscopy allows for a reliable and quantitative extraction of the electron-phonon coupling strength without requiring an effective temperature model or making strong assumptions about the underlying bare electronic band dispersion. Show Partial Abstract