Hi! Anthropologist here. When people talk about the FOXP2 gene, we believe the skill associated with it is actually sentence-construction. That means being able to put words together and "predict" what the end result will be. That might be distinctive wording or the cumulative meaning, etc. It's more about the mental math required to have a composite.

We know this because the FOXP2 gene is also used in tool-making, specifically knapping. Which is how you get spear heads and stone age tools. This process is very difficult and requires you to be able to "predict" how the stone will flake away. You have to be able to calculate angles visually and match your hand-eye coordination to achieve that result, many many times. It takes a while. This super-difficult skill is what we believe trained early homo groups (including Neanderthals) .

Lastly, we know that the culture of early homo groups was deeply spiritual. We know that shared identity was very important and that many early humans traveled in small family unit groups of 4-6 people. Early humans were prolific travelers and managed to explore the globe, leaving behind the nearly universal image of a religious carving. If I recall, it was an animal totem or some small vaguely humanoid sculpture, kind of like Venus of Willendorf. Basically, anthropologists never see anything that truly universal--because variety is the rule. But we found enough of these sculptures around the ancient world, all identical, all depicting shared group identity (humankind etc). This keepsake was traded globally, but also carried with many groups. From this, we know that their culture valued something even more than survival. We expect that shared communication and spirituality are the early adaptive skills of humans, which allowed us to assimilate the Neanderthals (genetically proven) and eventually take over the world.