Using a simple model of strong-field ionization of atoms that generalizes the well-known 3-step model from 1D to 3D, we show that the experimental photoelectron angular distributions resulting from laser ionization of xenon and argon display prominent structures that correspond to electrons that pass by their parent ion more than once before strongly scattering. The shape of these structures can be associated with the specific number of times the electron is driven past its parent ion in the laser field before scattering. Furthermore, a careful analysis of the cutoff energy of the structures allows us to experimentally measure the distance between the electron and ion at the moment of tunnel ionization. This work provides new physical insight into how atoms ionize in strong laser fields and has implications for further efforts to extract atomic and molecular dynamics from strong-field physics.