First, please note that this question seems to imply that the US is the only country that is “First World” today. This is most certainly not the case. We can certainly say that most countries of Western and Northern Europe are first world as are countries like Japan and Australia. The question, then, is whether still more countries will be joining the first world.
It seems likely that other countries will join this “club.” Strong economic development is being experienced in countries such as China and Brazil. These countries seem to be perhaps the most likely candidates to enter the first world. The question is whether these countries will achieve first world status any time soon. They are both rather far behind first world status at this point. China lacks the sort of political openness that is generally needed to join the first world. In addition, both might fall into what is called the “middle-income trap” where it is relatively easy for countries to climb out of poverty but it is hard for them to become truly wealthy.
Over time, it seems likely that other countries will enter the first world. Globalization is distributing wealth around the world much more broadly than was once the case. Countries are likely to become richer. As they do so, they are also likely to gain the sorts of social and political traits that are common to the first world.