Methods and systems are provided for pressurizing a transmission hydraulic circuit including a transmission mechanical pump coupled to an engine though a gearbox. One example method comprises, during an engine start, adjusting a speed ratio between the transmission pump and the engine between a first speed ratio and a second speed ratio, the pump rotating faster relative to the engine at the first speed ratio as compared with the second speed ratio. In this way, the pump may be driven at different speed ratios relative to the engine to provide better pressurization in the transmission.