Not yet! If your home was new , we would guess that the trim had shrunk. And for that reason we would not be concerned about shifting, and we would concur with your suggested fix. In this case, patience is in order.

First, silicone caulk the opening to prevent water damage to the area. The silicone is pliable and will maintain a seal even if the gap changes slightly. As large as the gap is, the repair will look somewhat unsightly. Monitor the gap through this winter and into the summer. Look for movement at the joint as ground expansion and settlement occur with the changing seasons. If the settlement (which probably caused the gap) has stopped, then it would be most acceptable to glue in a wood block to patch the gap.

What we are worried about here is that once filled with a piece of wood, the gap in the sill will not close to its normal size if natural ground shift reverses, or if a repair is made to the floor below that offsets natural settlement. Time will tell this tale.