Within the strong-field approximation, we study the time-resolved ionization process of a hydrogen atom in strong laser fields. At any time during the interaction between an atom and a laser field, the electron may instantaneously absorb all possible energies and build a wide momentum spectrum. As the interaction evolves in time, the coherent superposition of all previous instantaneous ionization events gradually filters out all other energy components except the part with an energy $n\ensuremath{\omega}\ensuremath{-}{I}_{p}$, where ${I}_{p}$ is the ionization potential, $\ensuremath{\omega}$ is the photon energy, and $n$ is a positive integer. The establishment of the electron energy spectra in above-threshold ionization, rescattering, and streaking can all be directly viewed by tracking the time-dependent momentum spectra.