a simple question: when were the mishnah, tosefta, and talmud written and how do we know?
regarding mishnah and tosefta: most sources say that the mishnah was compiled by the end of 2nd century CE (by R. Yehudah HaNasi), and that the tosefta was compiled a bit later, probably by end of 3rd century CE (https://www.jewishvirtuallibrary.org/mishnah).
but how do we know this? are there handwritten manuscripts of these texts that can be dated to the 2nd or 3rd century CE? the earliest complete manuscript seems to be Kaufmann, which is dated to 10th or 11th century (https://en.wikipedia.org/wiki/Kaufmann_Manuscript). if there are no earlier manuscripts from the 2nd or 3rd centuries, then how do we know that these texts were written in this period?
regarding talmud: most sources say the talmud was written over a period of several hundred years after mishnah and compiled around 500 CE (https://www.bl.uk/collection-items/first-complete-mishnah). however, the earliest printings of these books are from several centuries later (16th century), which again raises the question of: how do we know the talmud was definitively written between 200-500 CE, which is the usual range quoted in sources?