An experimental continuous-wave (cw) pump-probe scheme is demonstrated by investigating the population and photoionization dynamics of an atomic system. Specifically, $^6$Li atoms are initially prepared in optically pumped $2^{2}S_{1/2}$ and $2^{2}P_{3/2}$ states before being excited via multi-photon absorption from a tunable femtosecond laser. The subsequent cascade back to the ground state is analyzed by ionizing the atoms in the field of a cw optical dipole trap laser. Conventional spectroscopic methods such as standard cold-target recoil-ion momentum spectroscopy (COLTRIMS) or velocity map imaging (VMI) cannot provide simultaneous momentum and time-resolved information on an event-by-event basis for the system investigated here. The new approach overcomes this limitation by leveraging electron-recoil ion coincidences, momentum conservation, and the cyclotron motion of the photoelectron in the magnetic spectrometer field. This enables the reconstruction of ionization times and time-of-flight of the charged target fragments with nanosecond resolution. As a result, not only can three-dimensional photoelectron momentum vectors be determined, but the (incoherent) population dynamics of the atomic system also become accessible. Future applications exploring coherent atomic dynamics on the nanosecond timescale would not only expand the scope of time-resolved spectroscopy but can also aid in developing coherent control schemes for precise atomic manipulation.