  Despite its simple structure and low degree of electronic correlation,
SrTiO$_3$ (STO) features collective phenomena linked to charge transport and,
ultimately, superconductivity, that are not yet fully explained. Thus, a better
insight in the nature of the quasiparticles shaping the electronic and
conduction properties of STO is needed. We studied the low energy excitations
of bulk STO and of the LaAlO$_{3}$/SrTiO$_{3}$ two dimensional electron gas
(2DEG) by Ti L$_3$ edge resonant inelastic x-ray scattering. In all samples, we
find the hallmark of polarons in the form of intense $dd$+phonon excitations,
and a decrease of the LO3-mode electron-phonon coupling when going from
insulating to highly conducting STO single crystals and heterostructures. Both
results are attributed to the dynamic screening of the large polaron
self-induced polarization, showing that the low temperature physics of STO and
STO-based 2DEGs is dominated by large polaron quasiparticles.
