What (if any) are the structural similarities that all languages share that allows them to be taken in and learned by virtually all humans starting at a very young age?
For any specific property you suggest, there's probably a counter-example somewhere. However, the big one that's most often considered universal is recursion.
Every known human language (*) has recursion: some way of embedding one clause into another one, to an arbitrary depth. In English, you can use relative clauses, like "I saw the man who saw the woman who saw…", or complementizers, like "I told Alice that Bob told Claire that…". And while the exact mechanics differ, every language has some way of doing this.
(*) There's one often-cited counterexample, Pirahã. However, the work claiming that Pirahã lacks recursion is…controversial. Nobody except the original researcher has been able to check the evidence, and Pirahã is claimed to have quite a lot of properties that are unlike any other language on Earth. It seems more reasonable to treat it as a bad data point.