This can be regarded as the grammar of a specific language GR, but unlike the grammar of a spoken languages, the grammar of GR is universal. The baby is like other people. It can learn about its own capabilities from observing others, and it can learn about others by putting itself in their places. It would be interesting if there were innate non-linguistic human mental abilities that are not present in animals. Nothing appears obvious, but maybe the innate part of human number sense is qualitatively different from that of animals.
Some abilities require early experience to acquire.
For example, people blind from birth who gain sight as adults don't acquire an image processing system fully adapted to the world as it is. However, there is no reason to expect that they could acquire an image processing system adapted to a quite different visual world. If this is so, then the image processing system is still basically innate.