An assembly is provided for a turbine engine. This turbine engine assembly includes a rotating structure, a stationary structure, a bearing and a gearbox. The rotating structure is configured to rotate about a rotational axis. The rotating structure includes a shaft and a bladed rotor connected to the shaft. The stationary structure circumscribes the rotating structure. The bearing rotatably mounts the shaft to the stationary structure. The gearbox is disposed radially inboard of the bearing.