Much of traditional folklore studies – as partially established/inspired by Jacob Grimm – was intended to address this question. The intellectual response to the effort to understand the earlier history of folktales as documented by the Brothers Grimm was the Finnish Historic Geographic Method.

Proponents of this approach arrived at a tale type index, beginning with the work of Aarne Thompson, and then augmented by the American Stith Thompson, and then the German, Hans-Jörg Uther. Earlier references consequently refer to folktale types as “AT” followed by a number: AT 306, The Twelve Dancing Princesses, is a folktale I studied while researching at the Irish folklore archives. Now, in recognition of the enormous contribution of Uther, tale types are referred to as “ATU.”

For examples of the way variants are organized and considered, see this site. The tale type index allows for the identification and organization of international variants of various folktales. It is then possible to identify variants in historical documents.

By considering all the variants of a tale type it is possible to understand the history and spread of each tale type. This begins with the collection of variants documented across the map (geographical) as recorded by folklore collecting in recent centuries. This is then compared with historical documents, and by considering how variations appeared and spread across space and through time, there was/is an effort to understand the age of a tale type and its likely place of origin.

There are critics of this method, but at its core, it continues to be used to understand the history of the various folktale types, many of which appeared in the collections published by the Brothers Grimm.

Edit: because of this method and decades of study, we have a fairly good idea of the history of these folktale types – although some types have been studied more thoroughly than others. As with any historical enquiry, these is often debate about the conclusions that scholars have reached – which way a folktale diffused, where and when it originated etc., but overall, the method is respected among many (but not all) folklorists.