There were predecessors to pencils going back hundreds of years before that, with very similar capabilities. They used soft metals that streak when dragged across a surface, particularly silver and lead (Pb) (also the etymology of "pencil lead"); and sharpened these into narrow points. The modern pencil sort of iterated on those ideas. Soft graphite powder, in a wax binder, leaves a streak superior to metals; and encasing it in wood was the solution to the graphite composite's brittleness.

https://en.wikipedia.org/wiki/Silverpoint

Here's a zoomable example by da Vinci (don't you agree they look awfully similar to pencil lines?)

https://www.britishmuseum.org/collection/object/P_1860-0616-...

Henry Petroski wrote a great book about the history of the pencil. There used to be a mine in Southern England which contained pure graphite, that was found in the 16th century. That graphite could just be cut into sticks and made into writing implements. The modern pencil consisting of powdered graphite with a binder is a response to that mine being exhausted. So it's a substitute for a product that wasn't possible before that pure deposit was found.

A pencil is essentially a core of something that easily rubs off onto other things surrounded in a protective cladding of something that keeps it from rubbing off onto your hands; stuff like this has existed for centuries.

There is essentially only one place in the world where graphite suitable for pencils naturally exists, and this wasn't discovered until the 1500s. Making it artificially from powdered graphite was first done in 1662, and the first process that approximates modern pencil construction was done in 1795, which is probably what you're calling the invention of the pencil.

The ancients had reed/bamboo pens, which looked similar to modern pencils, though they were largely supplanted by quill pens by medieval times.