Efforts to detect low-mass exoplanets using stellar radial velocities (RVs) are currently limited by magnetic photospheric activity.Suppression of convective blueshift is the dominant magnetic contribution to RV variability in low-activity Sun-like stars. Due to convective plasma motion, the magnitude of RV contributions from the suppression of convective blueshift is related to the depth of formation of photospheric spectral lines for a given species used to compute theRV time series. Meunier et al. used this relation to demonstrate a method for spectroscopic extraction of the suppression of convective blueshift in order to isolate RV contributions, including planetary RVs, that contribute equally to the time series for each spectral line. Here, we extract disk-integrated solar RVs from observations over a 2.5 yr time span made with the solar telescope integrated with the HARPS-N spectrograph at the Telescopio Nazionale Galileo (La Palma, CanaryIslands, Spain). We apply the methods outlined by Meunier et al. We are not, however, able to isolate physically meaningful contributions due to the suppression of convective blueshift from this solar data set, potentially because our data set is taken during solar minimum when the suppression of convective blueshift may not sufficiently dominate activity contributions to RVs. This result indicates that, for low-activity Sun-like stars, one must include additional RV contributions from activity sources not considered in the Meunier et al.model at different timescales, as well as instrumental variation, in order to reach the sub meter per second RV sensitivity necessary to detect low-mass planets in orbit around Sun-like stars.