The so-called minimal models of unconventional superconductivity are lattice models of interacting electrons derived from materials in which electron pairing arises from purely repulsive interactions. Showing unambiguously that a minimal model actually can have a superconducting ground state remains a challenge at nonperturbative interactions. We make a significant step in this direction by computing ground states of the 2D U-V Hubbard model—the minimal model of the quasi-1D superconductors—by parallelized DMRG, which allows for systematic control of any bias and that is sign-problem-free. Using distributed-memory supercomputers and leveraging the advantages of the U-V model, we can treat unprecedented sizes of 2D strips and extrapolate their spin gap both to zero approximation error and the thermodynamic limit. Our results for the spin gap are shown to be compatible with a spin excitation spectrum that is either fully gapped or has zeros only in discrete points, and conversely that a Fermi liquid or magnetically ordered ground state is incompatible with them. Coupled with the enhancement to short-range correlations that we find exclusively in the dxy pairing channel, this allows us to build an indirect case for the ground state of this model having superconducting order in the full 2D limit, and ruling out the other main possible phases, magnetic orders, and Fermi liquids.