  We study how polaronic states form as a function of time due to strong
electron-phonon coupling, starting from a hot electron distribution which is
representative of a photo-induced metallic state immediately after laser
excitation. For this purpose we provide the exact solution of the
single-electron Holstein model within nonequilibrium dynamical mean-field
theory. In particular, this allows us to reveal key features of the transient
metallic state in the numerically most challenging regime, the adiabatic
regime, in which phonon frequencies are smaller than the electronic bandwidth:
Initial coherent phonon oscillations are strongly damped, leaving the system in
a mixture of excited polaron states and metastable delocalized states. We
compute the time-resolved photoemission spectrum, which allows to disentangle
two contributions. The existence of long-lived delocalized states suggest ways
to externally control transient properties of photo-doped metals.
