As a piper, I do get asked this sometimes and occasionally it seems to mean, "why would anyone ever make bagpipes?". We do have a pretty good idea of the basic evolution for them, however.

First, it's not hard to create a reed instrument. Marsh grasses like Arundo Donax can have hollow canes that are quite long. Splitting the side of a length right below a node, so its got a lip, like these , creates musical reed- put it into your mouth and blow and it plays a note. If you take a long length of cane and cut the end like that, you end up with a pipe that makes low sound: cut the length shorter and it makes a higher sound. Now ,one nice thing about cane reed instruments like this is that they don't take nearly as much wind as something like a flute, but they do take some pressure. Eventually people figured out circular breathing: you can inflate your cheeks and push air out of your mouth, while closing off the back of your throat and breathing in through your nose, and in this way you can keep a reed pipe going on and on. If you punch holes in the side of the pipe, so you can play different notes with your fingers, it might occur to you to put another reed pipe in your mouth as well. The possibilities for this technique can be seen in the Sardinian Launeddas, played here by maestro Luigi Lai

Something like this is the best guess we also have for the original hornpipe or pibcorn, though it may have had a windcap to press against and reinforce the mouth, because the muscles around the lips have a hard time holding the pressure for long periods of time. At any rate, simple split-cane reed instruments like this are still played in the Middle East, and probably they originated there. But it would have been quite early: the double-pipes, or aulos, shown being played on ancient Greek pottery were likely reed instruments, as they're often shown tied to the player's head so the mouth did not have to support the pressure. So the origins of the double-reed pipe could really be lost back in the mists of time...( must be just full of things by now, those mists).

Eventually someone thought to replace the cheeks of their mouth with something bag-like. I am not sure if the dating is settled, as descriptions of ancient instruments can be quite vague. Sometimes we have no more than the etymology of a name: like, it's hard to figure out if the Greek "symphonia" ( "multi-voice") is a a double pipe or pipe organ or even a stringed instrument. Sibyl Marcuse's instrument encyclopedia states that bagpipes were known to the Romans in the 1st c. AD. but supplies no specific reference for that. But certainly in medieval Europe there were bagpipes by the 13th c. : the Cantigas de Santa Maria shows bagpipers, as well as a similar instrument called the bladderpipe . It is tempting to see the bladderpipe as an intermediate stage, between stuffing your cheeks with reed pipes and setting them into a bag squeezed under your arm....but I don't think it's been proven to be that: it's possible they were another solution to the problem of playing a reed pipe without really working your mouth hard..

A decent more detailed reference for this question is Anthony Baines' Woodwind Instruments and their History. Bagpipes have a quite diverse and debated history ( like how the French created a cute complex little bagpipe for the nobility to use when playing at being shepherds, which later became the bellows-blown Northumbrian and Irish Uillean pipes) but Baines is still good for the basic family tree, perhaps because he was bassoon player and liked reeds, didn't think bagpipes were beneath notice.