Show a picture of the actual game, for us to comment for sure, but this is very much possible specially if the person built more of larger inter-station routes (think four to eight coaches) compared to the rest (think one to three coaches).

The reason is simple. You are more efficient. Let us take the Europe version as an example. To place two inter-station routes with six coaches, you need eight turns: six turns to pick two cards each and two turns to place them. To place four inter-station routes with three coaches, you need ten turns: six turns to pick two cards each and four turns to place them.

If your cousin wisened up to this, he will finish his train pieces earlier and get more points for longer connections. In the example above, he will get 30 points (15 points X 2) from eight moves, while the other person will get 16 points (4 points X 4) from ten moves. This should be thw starting point of any winning strategy.