I know that original animes weren't based on light novels or mangas (see: this). However, I think there are some early shows that are based on mangas (Astro Boy for example, I think). What was the first anime based on a manga? Also, what was the first anime based on a light novel?
While not the most scientific method, one could generate a list of anime entries over at Anime News Network, sort it by order and see what is the earliest entry in their database that fits the criterion we're looking for. Here would be an example of such a list.
Obviously the service's database is most likely incomplete, but regardless, it is still an authoritative source for anime information, and given the size, and time range of the database, it can be trusted as a good estimation.