ATWATER, Calif.—Waymo LLC, the driverless-car unit of Google parent Alphabet Inc., demonstrated Monday what traveling in its minivans might be like as a fully autonomous ride-hailing service.

The experience begins in the back seat of the Chrysler Pacifica, where screens welcome customers aboard and instruct them to push a blue “start ride” button on the ceiling. The van otherwise seems like any other, except for its empty front seats.

The...