Astronomers Say They Have Spotted
the Universe’s First Stars
If that is the case, we can see only an infinite small fraction of the stars in the universe. Under that assumption, I find it hard to have a concept of what spotting the universe's first stars could mean.
The oldest stars among those that we can see?
Yes.
If I've understood the lectures correctly, time isn't really well-ordered, and on scales like this the deviation makes a substantial difference.
However, what we are looking at in cases like this is stars far enough away that the light took most of the age of the universe to reach us, so it's not unreasonable to call those stars (members of the set of) "the Universe’s First Stars".
The question is about the relationship between the age of the universe (well, after the big bang) and stars that came into existence afterwards. We have a pretty good idea how old the universe is, and with the universe expanding, light from the early days of the universe still makes it to earth from billions of light-years away.
But for similar reasons, unless some fundamental understanding of time and space changes, nothing outside the visible universe really matters.