If you understand how stars work, you can observe the physical properties of one of them and extrapolate its age, and know when it had to have been born.
Stars undergo a lot of changes as they age: their radius, luminosity, and temperature all evolve as they burn through their fuel. But a star’s lifespan, in general, is dependent on only two properties that it’s born with: its mass and its metallicity, which is the amount of elements heavier than hydrogen and helium present within.
The oldest stars we’ve found in the Universe are nearly pristine, where almost 100% of what makes them up is the hydrogen and helium left over from the Big Bang. They come in at over 13 billion years old, with the oldest at 14.5 billion. And this is a big problem, because the Universe itself is only 13.8 billion years old.