All that partitioning and counting can only be performed by a system that is able to abstract and differentiate between different abstractions. Brains and computers appear to be good at this, but other than that, I don't see many other structures that are capable of doing this.
So, no, I don't observe numbers in the universe, if I take on the perspective of, say, a rock.
That's like asking "where in nature does one observe numbers"?
Literally everywhere.
Your jug partitions water into the set inside the jug and the set outside it.
Caves are a subset of rock formations.