  Multi-orbital electronic models hosting a non-trivial band-topology in the
regime of strong electronic interactions are an ideal playground for exploring
a host of complex phenomenology. We consider here a sign-problem-free and
time-reversal symmetric model with isolated topological (chern) bands involving
both spin and valley degrees of freedom in the presence of a class of repulsive
electronic interactions. Using a combination of numerically exact quantum Monte
Carlo computations and analytical field-theoretic considerations we analyze the
phase-diagram as a function of the flat-band filling, temperature and relative
interaction strength. The low-energy physics is described in terms of a set of
intertwined orders -- a spin-valley hall (SVH) insulator and a spin-singlet
superconductor (SC). Our low-temperature phase diagram can be understood in
terms of an effective SO(4) pseudo-spin non-linear sigma model. Our work paves
the way for building more refined and minimal models of realistic materials,
including moir\'e systems, to study the universal aspects of competing
insulating phases and superconductivity in the presence of non-trivial
band-topology.
