Restarting car after popping the clutch...

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Sometimes when I'm at a light and it turns green I'll accidentally pop the clutch and the car will die. I think all 5-speed Yaris owners know how finicky the clutch is. When I try to restart it by turning the ignition key, nothing happens.

I'm not positive of exactly what I do because I tend to panic when there are people behind me waiting to go. But from what I can remember, I'll push on the brake pedal, let go of the brake pedal, push on the clutch, put the shifter back in neutral, push the handbrake up. Not exactly in that order, but idk. I eventually get the car started again, but I'm just wondering what exactly I need to do to get the car started up or if anyone knows why the car doesn't want to start up right away. No manual cars have ever given me so much trouble starting back up after popping the clutch. Usually, as long as you have the clutch fully depressed a manual car will just start up. Anyone got any ideas?