I linked in the comments to the question to an article by Dan Rabinowitz published by Hakirah journal regarding Jewish sources pertaining to the origin of the nekudos. [Note that although the taamim of the Tanach are not mentioned throughout the article, it seems implicit in most of the sources (and in the main source, actually explicit) that the same applies to the taamim.] The gist of it is as follows:
The earliest sources to be found are those that address why our Torah scrolls lack the vowel symbols. The split begins here.
- Machzor Vitri (11th Century) cites an anonymous "t'shuvas hagaon" who writes that the original Torah scrolls did not have vowels for the nekudos did not exist at the time. Even when they were later invented, we keep our official Torah scrolls emulating the originals.
- Radbaz (16th Century) believes that the nekudos were received as part of the oral tradition at Sinai, but were not included in the main text to allow for mystical and esoteric readings of the text that often rely on attributing different vowels to various words.
The first source to directly address the history of the nekudos after the above citations was R' Eliyahu HaBachur in Mesoras HaMasores (16th Century). He demonstrated that nekudos in the Hebrew language did not exist until after the close of the Talmudic era. Certainly not "Sinaitic". (It is worth noting that HaBachur explicitly claims that he finds no contradictions between this view and any statements of Chazal or the Zohar.)
After that, it becomes a matter of who agrees with HaBachur and who (often vehemently) disagrees. The Zohar here becomes a central issue, being that it clearly employs the use of the nekudos. If one agrees with HaBachur, they must admit that parts of the Zohar are at the very least post-Talmudic. Indeed, the sources that agree are found in anti-Zoharic works (by which I mean sources arguing the late dating of the Zohar).
On the other hand, those disagreeing with HaBachur use the Zohar as their main argument, taking as a given that it was composed in the Tannaitic era.
Those who agreed with R' Eliyahu HaBachur as to the late origins of the nekudos:
- R' Yaakov Emden (Mitpachas Sefarim)
- R' Samuel David Luzzatto (Vikuach al Chochmas HaKabbala)
Those who disagreed and maintained that the nekudos were received at Sinai (i.e. existed at the time of Matan Torah):
- R' Azariah de Rossi (Meor Einayim)
- Chida (Shem HaG'dolim)
- R' Moses Mendelssohn (Introduction to the Biur)
- R' Moses Kunitz (Ben Yochai)
- R' Shlomo Schick (Torah Sh'leimah)