Is turning on the headlights before starting a factory feature?

Not sure what you mean. The Corolla has day-time running lights, the are on when the engine is running. Always. Then, during darkness, the headlamps and tail lights come on automatically. Be sure to never cover that sensor on the dash by the windshield also. OR you can manually turn on the lights: on the turn signal lever by rotating it. Push forward or pull back for bright/dim. Pull the turn signal lever toward you and hold it of you feel the need to flash bright lights at somebody, day or night. BUT I am aware I did not answer you question, because I don't understand it

With the daytime running lights, they will come on when you turn key to the on position without the engine running.

Point taken Wayne, thanks, I did not make that clear. You are correct. The engine does not have to be running