  We carry out large-scale quantum Monte Carlo simulations of a candidate field
theory for the onset of superconductivity in magic-angle twisted bilayer
graphene. The correlated insulating state at charge neutrality spontaneously
breaks U(1) Moir\'e valley symmetry. Owing to the topological nature of the
bands, skyrmion defects of the order parameter carry charge $2e$ and condense
upon doping. In our calculations we encode the U(1) symmetry by an internal
degree of freedom such that it is not broken upon lattice regularization.
Furthermore, the skyrmion carries the same charge. The nature of the
doping-induced phase transitions depends on the strength of the easy-plane
anisotropy that reduces the SU(2) valley symmetry to U(1) $\times \mathbb{Z}_2
$. For large anisotropy, we observe two distinct transitions separated by phase
coexistence. While the insulator to superconducting transition is of mean-field
character, the U(1) transition is consistent with three-dimensional XY
criticality. Hence, the coupling between the gapless charge excitations of the
superconducting phase and the XY order parameter is irrelevant. At small
anisotropy, we observe a first-order transition characterized by phase
separation.
