  The search for hidden orders in photoexcited lattice systems is an active
research field driven by experimental reports of light-induced or
light-stabilized phases. In this study, we investigate hidden electronic orders
in strongly correlated two-orbital Hubbard models with orbital-dependent
bandwidths. In equilibrium, the half-filled systems are antiferromagnetically
ordered. Using non-equilibrium dynamical mean field theory we demonstrate the
appearance of nonthermal ferromagnetic order in the photo-doped state, if the
two bandwidths are sufficiently different, and its coexistence with
spin-singlet $\eta$-superconductivity in the high photo-doping region.
Spin-triplet $\eta$-superconducting order appears instead if the two bandwidths
are comparable. The rich nonequilibrium phasediagram uncovered in this work
shows that Mott insulating multi-orbital systems provide an interesting
platform for the realization of nonthermal electronic orders.
