Writing has only been independently invented for languages a handful of times. Basque does not seem to be one of them.

If Basque ever had an independent writing system, we have no trace of it. As it is, we have precious few traces of any kind of Basque before the Middle Ages: namely topological names, names of people that are mentioned in inscriptions or literary works, and these are often mentioned through other languages: Latin, early forms of Romance written with the Latin alphabet etc.

Let me remind you that most languages have never been written down because the technology of writing was never invented, never reached them, or reached them but was lost or abandoned. It is not at all surprising.

As it is, Basque literary activity was scarce right up until the 20th century, and you could pretty much say that Basque literary work before then was limited to religious works, translations of Bibles, homilies and things of that sort, as most people in the world was illiterate in their language before national education. In the Basque Country the ones who could read were usually priests and they weren't going to publish much else.

Publishing a book was difficult and costly: to whom would a book be addressed to anyway, if there was precious few people to buy and read the books?

Also you must keep in mind that Basque shows a stunning array of dialectalisation, probably with its origin in the Middle Ages due to the political fragmentation of the Basque Country, and thus this would also impede literary efforts, as authors who limit themselves to intra-regional koines, further restricting a reading audience. Indeed before the universal standardisation of the language in the mid 20th century (!!!), there were multiple regional standards.

You'd also have to keep in mind that for the vast majority of Basque's history, Basque elites were literate in other languages. Why write in Basque when they knew Latin, and then Navarro-Aragonese (to be replaced by Spanish) or French?