A vehicle includes an engine, a continuously variable transmission including an input shaft coupled to the engine, an output shaft, an electric machine, and a gearing arrangement. The electric machine is configured to actuate the gearing arrangement to change a speed ratio between the input and output shafts. A controller is programmed to, responsive to a request to manually shift the transmission to one of a predetermined number of virtual discrete speed ratios and the engine being OFF, command starting of the engine regardless of a driver-demand torque and operate the electric machine to shift the transmission to the one of the speed ratios.