Systems and methods for controlling an engine start in a hybrid vehicle

A system for a vehicle, comprising:

• an engine;
• a transmission selectively coupled to the engine via two clutches, the transmission including one or more shifting elements;
• an electric machine positioned downstream of the transmission;
• an electric transmission oil pump;
• and
• a controller storing instructions in non-transitory memory that, when executed, cause the controller to:
• propel the vehicle via the electric machine while the engine is disconnected from the transmission via the two clutches being fully open;
• pre-engage a first target gear of the transmission and a first non-target gear of the transmission while propelling the vehicle solely via the electric machine, selecting the first non-target gear in response to accelerator pedal position and vehicle speed, and starting the engine in response to a driveline torque request that exceeds a capability of the electric machine, and where pre-engaging the first target gear and the first non-target gear includes operating the electric transmission oil pump to provide hydraulic pressure to control the one or more shifting elements to pre-engage the first target gear and the first non-target gear.