  We exploit a time-resolved pump-probe spectroscopic technique to study the
out-of-equilibrium dynamics of an ultracold two-component Fermi gas,
selectively quenched to strong repulsion along the upper branch of a broad
Feshbach resonance. For critical interactions, we find the rapid growth of
short-range anti-correlations between repulsive fermions to initially overcome
concurrent pairing processes. At longer evolution times, these two competing
mechanisms appear to macroscopically coexist in a short-range correlated state
of fermions and pairs, unforeseen thus far. Our work provides fundamental
insights into the fate of a repulsive Fermi gas, and offers new perspectives
towards the exploration of complex dynamical regimes of fermionic matter.
