Well, this is usually where you can make up alot of positions. In league races the T1 isn't quite as bad as Public servers, reason being - everyone in league races
can drive (most of the time) and actually want to finish.
I'm actually going to disagree with most of you here..
When I'm going through the lap, starting from midfeild or the rear, I usually try to find the gaps and drive through them. Everyone wants to follow each other, but if you can find a gap, inside of outside, alot of the time you can make up 2 or 3 postions. You have to be careful when doing this though, and look left/right and use your mirrors alot. If you do not, this is when accidents happen.
If you back off/hesitate, that's when you get crashed. There's people behind you trying to go too fast, and you're trying to go too slow.
If you just take it at a normal speed, a little slower than race speed you should survive.
If you're too agressive, you may crash, if you're not agressive enough, you may get crashed. Also you have to be thinking of your actions to others eg:
Going into t1, you brake
car behind you brakes too late
car behind hits you
you go nuts and shit hits the fan
To solve this problem you could (or should) have run a little wider and let off the brakes slightly, so the other car wouldn't rear end you. He will most likely run wide and you can gain this position back up.
It basically comes down to taking calculated risks, looking left/right and using your mirrors, that's it basically.