  We investigate phonon-mediated Cooper pairing in flat electronic band systems
by solving the full-bandwidth multiband Eliashberg equations for
superconductivity in magic angle twisted bilayer graphene using a realistic
tight-binding model. We find that Cooper pairing away from the Fermi level
contributes decisively to superconductivity by enhancing the critical
temperature and ensures a robust finite superfluid density. We show that this
pairing yields particle-hole asymmetric superconducting domes in the
temperature-gating phase diagram and gives rise to distinct spectroscopic
signatures in the superconducting state. We predict several such features in
tunneling and angle resolved photoemission spectra for future experiments.
