  We investigate the excitation spectrum of strongly correlated sodium
cobaltate within a realistic many-body description beyond dynamical mean-field
theory (DMFT). At lower doping around $x$=0.3, rather close to Mott-critical
half-filling, the single-particle spectral function of Na$_x$CoO$_2$ displays
an upper Hubbard band which is captured within DMFT. Momentum-dependent
self-energy effects beyond DMFT become dominant at higher doping. Around a
doping level of $x\sim 0.67$, the incoherent excitations give way to
finite-energy spin-polaron excitations in close agreement with optics
experiments. These excitations are a direct consequence of the formation of
bound states between quasiparticles and paramagnons in the proximity to
in-plane ferromagnetic ordering.
