Methods and systems are provided for improving engine restart operations responsive to a heavy operator pedal tip-in. Engine torque and disconnect clutch capacity are controlled during cranking and engine speed run-up so as to provide excess torque to accelerate the engine to the motor speed and prepare the engine for elevated torque delivery after the engine connects to the driveline. At a time of connecting the engine to the driveline, the engine torque is transiently reduced to avert NVH issues related to engine speed overshooting or undershooting the target speed.