Yes. This is applicable only to later players, like players 3 or 4, on the first round. But, if on your first play someone else is unable to play, there is a marker on their train to indicate it is open, and a domino played before you allows you to, you can play on another's player's train before your own. However, some house rules require people to play on their own train first and if they fail to do so, they must place a marker on their train and the next player can play on your train. Agree to these rules before starting.