A better molecular-level understanding of Li+ diffusion through ceramic/polymer interfaces is key to design high-performance composite solid-state electrolytes for all-solid-state batteries. By considering as a case study a composite electrolyte constituted by Li+ conductive Ga3+ doped-Li7La3Zr2O12 (LLZO) garnet fillers embedded within a poly(ethylene oxide) and lithium bis(trifluoromethanesulfonyl) imide polymer matrix (PEO(LiTFSI)), we investigate Li+ interfacial dynamics at conditions of high polymer confinement, with large filler particles in a fully amorphous polymer phase. Such confinement scenario is aimed to capture the conditions near the percolation threshold, at which conductivity enhancement is often reported. Using molecular dynamics simulations combined with the generalized shadow hybrid Monte Carlo method and umbrella sampling calculations, we explain why the hopping towards the polymer phase of the Li+ sitting on the LLZO surface is thermodynamically hindered, while hopping of Li+ from the polymer to the LLZO is kinetically slowed-down by rigidified polymer near the interface. In addition, we demonstrate how the overlap of LLZO-bound polymer chains at high confinement leads to a decrease of Li+ diffusivity within the interstitial space. We put forward that these insights are relevant to interpret the variation of ionic conductivity as a function of volume fraction and filler particle sizes also below the glass transition temperature of the polymer, at the typical operating conditions of lithium ion batteries.