Life as we know it, namely here on Earth, is carbon-based, which means that the molecules that make up our cells contain carbon bonded with something else, primarily oxygen, hydrogen, and nitrogen. In the earliest age of the universe, hydrogen was extremely common, but none of these other elements. Helium was common as well, and the first generation of stars consisted of these two elements. So when those stars went supernova and exploded, they gave rise to a second generation of stars, as well as the materials needed for the formation of planets.
Some of the oldest stars out there are known as CEMP, or carbon-enhanced metal poor stars, which have far less iron and other heavy metals than our own sun. Our own planet formed during a period when heavy metals were much more common in space, but early planets, which might have supported life, would have consisted mainly of graphite, carbides, and diamond.
Because they contained carbon, and may have also been home to the other building blocks of life, planets such as these could have been the fist habitable planets out there. But life on them would have been very different than it is on Earth. From here, those planets would look quite similar to ours, being about the same size and mass, but they would have very different chemical compositions, especially in their atmosphere. So the trick is to look for such planets by looking first for old CEMP stars, and then using the transit technique, which locates planets by looking for the tell tale signs that they passed in front of a star. That method also tells us a lot about the chemical composition of the body passing in front of the star.
We don’t actually know if such planets are out there, as this is all conjecture at this point, but we’re already looking for planets anyway, so we might as well see if they’re out there.