The paper proposes a theory to explain how weak phonon-mediated interactions (J_A = 1-4 meV) can overcome strong Coulomb repulsion (U = 30-60 meV) in magic-angle twisted bilayer graphene (MATBG) to achieve superconductivity. The pairing mechanism is similar to that in A_2C_60 molecular superconductors, where optical phonons dynamically lift the degeneracy of moiré orbitals, analogously to the dynamical Jahn-Teller effect. This induced J_A, in the form of an inter-valley anti-Hund's coupling, is less suppressed by Kondo screening near a Mott insulator. The authors also consider an intra-orbital Hund's coupling J_H, which originates from the on-site repulsion of carbon atoms. Under a reasonable approximation, they prove that the renormalized local interaction between quasi-particles has a pairing channel in a doped correlated insulator at ν = ±(2 + δν), despite the bare interaction being positive definite. The existence of an optimal U for superconductivity is predicted. In a large parameter space of J_A and J_H, the ground state is found to have a nematic d-wave singlet pairing, which can lead to a p-wave-like nodal structure due to Berry's phase on Fermi surfaces. The study uses the topological heavy fermion model and Ward identities to analyze the pairing instability in the Fermi liquid phase at ν = -2 - δν, demonstrating the effectiveness of the flattened interaction approximation. Mean-field calculations confirm the presence of inter-valley d-wave pairing and suggest an optimal pairing strength and Coulomb interaction for superconductivity.The paper proposes a theory to explain how weak phonon-mediated interactions (J_A = 1-4 meV) can overcome strong Coulomb repulsion (U = 30-60 meV) in magic-angle twisted bilayer graphene (MATBG) to achieve superconductivity. The pairing mechanism is similar to that in A_2C_60 molecular superconductors, where optical phonons dynamically lift the degeneracy of moiré orbitals, analogously to the dynamical Jahn-Teller effect. This induced J_A, in the form of an inter-valley anti-Hund's coupling, is less suppressed by Kondo screening near a Mott insulator. The authors also consider an intra-orbital Hund's coupling J_H, which originates from the on-site repulsion of carbon atoms. Under a reasonable approximation, they prove that the renormalized local interaction between quasi-particles has a pairing channel in a doped correlated insulator at ν = ±(2 + δν), despite the bare interaction being positive definite. The existence of an optimal U for superconductivity is predicted. In a large parameter space of J_A and J_H, the ground state is found to have a nematic d-wave singlet pairing, which can lead to a p-wave-like nodal structure due to Berry's phase on Fermi surfaces. The study uses the topological heavy fermion model and Ward identities to analyze the pairing instability in the Fermi liquid phase at ν = -2 - δν, demonstrating the effectiveness of the flattened interaction approximation. Mean-field calculations confirm the presence of inter-valley d-wave pairing and suggest an optimal pairing strength and Coulomb interaction for superconductivity.