A system includes a catalyst for receiving and treating exhaust gas generated by an engine, a passive NOx adsorber (PNA) positioned upstream of the catalyst, a bypass valve positioned upstream of the catalyst and the PNA, and a controller. The controller is configured to: while controlling the bypass valve to direct exhaust gas to the PNA, detect a torque demand that is greater than a threshold value; responsive to detecting that the torque demand is greater than the threshold value, engage a motor, coupled with a battery system, with a drive shaft of the system to meet at least a portion of the torque demand; in response to the engagement of the motor with the drive shaft not meeting all of the torque demand, engage the engine with the drive shaft to meet a remainder of the torque demand.