Solar evolutionary models are thus far unable to reproduce spectroscopic, helioseismic, and neutrino constraints consistently, resulting in the so-called solar modeling problem. In parallel, planet formation models predict that the evolving composition of the protosolar disk, and thus, of the accreted gas by the proto-Sun must have been variable. We show that solar evolutionary models that include a realistic planet formation scenario lead to an increased core metallicity of up to 5%, implying that accurate neutrino flux measurements are sensitive to the initial stages of the formation of the Solar System. Models with homogeneous accretion match neutrino constraints to no better than 2.7{sigma}. In contrast, accretion with a variable composition due to planet formation processes, leading to metal-poor accretion of the last ~4% of the young Sun's total mass, yields solar models within 1.3{sigma} of all neutrino constraints. We thus demonstrate that in addition to increased opacities at the base of the convective envelope, the formation history of the Solar System constitutes a key element in resolving the current crisis of solar models.