  We propose a theory for how the weak phonon-mediated interaction ($J_{\rm
A}\!=\!1\!\sim\!4$meV) wins over the prohibitive Coulomb repulsion
($U\!=\!30\!\sim\!60$meV) and leads to a superconductor in magic-angle twisted
bilayer graphene (MATBG). We find the pairing mechanism akin to that in the
A$_3$C$_{60}$ family of molecular superconductors: Each AA stacking region of
MATBG resembles a C$_{60}$ molecule, in that optical phonons can dynamically
lift the degeneracy of the moir\'e orbitals, in analogy to the dynamical
Jahn-Teller effect. Such induced $J_{\rm A}$ has the form of an inter-valley
anti-Hund's coupling and is less suppressed than $U$ by the Kondo screening
near a Mott insulator. Additionally, we also considered an intra-orbital Hund's
coupling $J_{\rm H}$ that originates from the on-site repulsion of a carbon
atom. Under a reasonable approximation of the realistic model, we prove that
the renormalized local interaction between quasi-particles must have a pairing
(negative) channel in a doped correlated insulator at $\nu=\pm(2+\delta\nu)$,
albeit the bare interaction is positive definite. The proof is non-perturbative
and based on exact asymptotic behaviors of the vertex function imposed by Ward
identities. Existence of an optimal $U$ for superconductivity is predicted. We
also analyzed the pairing symmetry. In a large area of the parameter space of
$J_{\rm A}$, $J_{\rm H}$, the ground state has a nematic $d$-wave singlet
pairing, which, however, can lead to a $p$-wave-like nodal structure due to the
Berry's phase on Fermi surfaces (or Euler obstruction).
