I found this great old book in an Edinburgh library a few years ago, about the invention of cooking. It's called "Food in History" by Reay Tannahill, published 1975.
I copied out a fascinating couple of paragraphs, let me quote them here:
But how the process of boiling was discovered - as it appears to have been long before the invention of pottery or the development of metalworking techniques - is a much more difficult problem. Fire may turn up by accident, and roasting may be the equally accidental result. But hot water is a rare natural phenomenon, and cannot be produced either accidentally without containers which are both heatproof and waterproof.
It is usually argued that food in prehistoric times was boiled by the following method. A pit or depression in the earth was first lined with flat, overlapping stones, to prevent seepage, and then filled with water. The water was brought to the boil by heating other stones or pebbles directly in the hearthfire and manhandling them (by some unspecified means) into the water. While the food was cooking, more hot stones were added to keep the water at a suitable temperature. In fact, this pit method sounds like a late development, a mass catering technique designed for large social gatherings which may have been spread by migrating tribes of advanced peoples. These, passing through the territory of backward communities, would repay their hosts by giving a feast. The backward communities, impressed by the new boiled food, would imitate the method - and continue to imitate it - because it was the only one they knew. 5000 B.C. appears to be the earliest date at which there is proof that the technique was used.
Long before this, however, many widely scattered peoples had their own more logical and far less tiresome ways of boiling meat, making use of pre-pottery containers which not only allowed them to use water in their cooking but may even, in some cases, have inspired the idea - either because without some form of liquid the food would stick to the container, or because food cooked in them produced its own moisture in the form of juices or steam.
In many parts of the world, for example, large mollusc or reptile shells must have been used, as they still were in the Amazon in the nineteenth century, when the naturalist Henry Walter Bates sampled a dish made from the entrails of the turtle, "chopped up and made into a delicious soup called sarapatel, which is generally boiled in the concave upper shell of the animal."
In Asia, that productive tree, the bamboo, was probably used. A hollow section stoppered with clay at one end, filled with scraps of meat and a little liquid, then stoppered again at the other would answer the purpose well. The method is still used in Indonesia today.
In Central America, in the Tehuacan valley near the south-western corner of the Gulf of Mexico, the people who lived in rock shelters around 7000 B.C. and gathered wild maize for food had begun to use stone cooking pots. It seems likely that a pot, once made, was sited in the centre of the hearth and left there permanently. It would be very heavy, suitable for use only when a community was firmly fixed in its abode or willing to fashion a new pot each time it moved its cave.
Before the advent of pottery and bronze, there was at least one type of container which was widely distributed, waterproof, and heatproof enough to be hung over (if not in) the fire. This was an animal stomach. In paleolithic times, the hunter, having killed his prey and carved up the flesh for transport, rewarded himself with a banquet of the more perishable parts - the heart, the liver, the brain, the fat behind the eyeballs, and some of the soft internal organs. Like twentieth-century Eskimos, he may have regarded the partially digested stomach contents of his kill as a special treat. It would be a logical development, as his liking for cooked food became a habit, to cook the contents in one of the stomach bags, and finally to use the same container for other dishes, some of them not too far removed in their finished effect from the modern casserole.
As late as the fifth century B.C., the nomad Scythians still cooked their food in a stomach bag when they had no cauldron available. "They put all the flesh into the animal's paunch," said Herodotus, "mix water with it, and boil it like that over the bonefire. The bones burn very well, and the paunch easily contains all the meat once it has been stripped off. [The rumen of a twentieth-century cow has a capacity of thirty to forty gallons.] In this way an ox, or any other sacrificial beast, is ingeniously made to boil itself."
Lots more interesting detail in this chapter ("Food and Cooking before 10,000 B.C."), The focus in this passage is on boiling, coming after some earlier developments such as roasting although roasting "was wasteful because of the shrinkage inevitable with high-temperature cooking."
This book came out in 1975, and it seems it was re-issued in 2000, so you should be able to find a copy. I might get one too. Inventions such as the wheel are well-known cliches - similarly, there must have been so many little revolutions in prehistoric cooking. I wonder if the research on this prehistory has developed further.