A snake charmer was the first pipe?
Seriously, 'pipe' is too generalized since now you are looking at the ancestor of all the woodwinds, brass, panpipes and digeridoos of the world.
Of all the stuff above, I agree with the essayist in the Britannica who pointed out the importance of the discovery of a pipe with the beating reed well down in the pipe. This was found in an Egyptian tomb, so we have a "not later than" date for an important step. The bag in Roman times is another "not later than" discovery.

(Hmmm, I have been reading too many posts by Ian on narrowing down time of origin of songs).