I'm no lithographer, but it seems to me that making a die cast out of metal, wood or stone, which could be pressed in to clay tablets to produce copies of its textual contents, would be easier than making a printing press that worked with ink and paper. By carving reliefs of Cuneiform signs into blocks of wood and assembling them into frames, typesetting would have been possible with the technology of the early bronze age. Was any such typesetting practiced?
I am focusing on writing formed as impressions on a surface, as practiced with Cuneiform and Linear A. This is because the ink-and-paper printing press required precision metallurgy to manufacture, which would not be necessary for a stamp meant to write in clay by means of forming indentations or raised areas on the material's surface.
I am focusing on the idea of copying entire documents in a single motion, as opposed to individual ideogram stamps or the stylus itself, because of the asymptotic advantage conferred by the ability for costs to grow in proportion to the number of copies, instead of the number of written symbols. Mass distribution of information is a keystone of modern culture, and it is interesting to ask whether there were any examples of related technology in ancient times.
The following resources have not been found to document the existence of a clay imprint printing press:
The Wikipedia page about Cuneiform. https://en.wikipedia.org/wiki/Cuneiform
The Wikipedia page about the Phaistos disk - because it does not make it clear whether it was made with ideogram stamps at one hand movement per letter, or whether it was stamped out whole with a "document stamp" in accordance with the technological advantage of a printing press. https://en.wikipedia.org/wiki/Phaistos_Disc#Typography
This more detailed article about the Phaistos disk, which describes the letters as being made with "movable type," but also describes the tools used as "individual stamps," leaving ambiguous the question of whether a face was produced in one stamping motion or several. https://luwianstudies.org/the-phaistos-disc/