The spring phytoplankton bloom in the subpolar North Atlantic and the mechanisms controlling its evolution and onset have important consequences for marine ecosystems and carbon cycling. Submesoscale mixed layer eddies (MLEs) play a role in the onset of the bloom by creating localized stratification and alleviating phytoplankton light limitation; however, the importance of MLEs for phytoplankton in a turbulent surface mixed layer has not yet been examined. We explore the effect of MLEs on phytoplankton by simulating their trajectories with Lagrangian particles subject to turbulent vertical displacements in an MLE-resolving model. By tracking the light exposure of the simulated phytoplankton, we find that MLEs can advance the timing of the spring bloom by 1 to 2 weeks, depending on surface forcing conditions. The onset of the bloom is linked with the onset of positive heat fluxes, whether or not MLEs are present.