Can't a player make their first route 7 long and trigger the end of the game making for a really short game? This has happened a few times and each time it does the player doing this wins. Doesn't this break the game? I see no way the game prevents this rush to the finish.
No, if your first route was 7 long, you would simply receive the length 3 carriage.
Acquire new carriage
If the length of a player’s route is at least as long as the number on the next highest carriage, he takes the next highest
card. A player may not skip over a carriage card, even if his route is long enough.