No because “we” (the first Christians and the Jews during, and before, Christ’s time, including the Apostles) used the Septuagint which included all the books - those even that Christ quoted from, which the Hebrew Bible does not contain.
Quoting myself from a while ago (I’m terribly sorry if I sound like a broken record

):
Personally I don’t think that speaking of a fixed, closed ‘canon’ of Scripture in the context of the Second Temple era without any definition is proper.
For Jews - and Christians - at that time, our modern Bibles (a complete collection of books bound under one cover) would have been something strange. In those days the norm was for different books, or different categories of books, to have their own scrolls: so a typical synagogue library would have had a scroll or scrolls of the Torah, some Prophets, perhaps a few writings such as the Psalms, or even collections of snippets from different scriptures organized around a particular theme (a
testimonia). It probably would not have had included all the texts now in the protocanon (the undisputed OT books), and it might well have included some texts that were not part of that canon.
While some scholars think that the Palestinian ‘canon’ was not definitively fixed until much later in time (some propose a date as late as the 4th century AD), others argue that it was already more or less established by the 1st century BC. Still, that does not mean that the canon was closed: while Jews already had good guesses as to which books were authoritative, there was apparently nothing which prevented considering other books not included in this protocanon as being authoritative as well or expressing doubts about a few of the already-‘canonized’ books (such as Ecclesiastes and Song of Songs, as we have seen earlier).
After the death of Jesus, and of His Apostles, which was about 100 AD (John being the last), in a village just outside of Jerusalem (the village of Jamnia), the Sadducees (who were Rabbis, and enemies of Christ and did not believe in the resurrection, life-after-death, and angels, - see Acts 5:17-19), assembled a completely new version of the Jewish Scripture, omitting some books entirely and rewriting others. The result is the Jamnian Canon, or the Palestinian Talmud. There is also another version known as the Babylonian Talmud.
No, it was the Pharisees. Or rather their later spiritual progeny the Rabbis. The Sadducees seem to have died out with the Temple.

And no, the
Talmud is really a work which combines the codified Oral Law, the
Mishnah (ca. 2nd-3rd century), and later explanations of and comments about it known as the
Gemara (ca. 4th-6th century). (Yes, they do exist in two versions: the Jerusalem and the Babylonian, with the Babylonian being the ‘standard’ version.)
And also, about the “council of Jamnia:” we should be careful not to inject the Christian idea of what a ‘council’ is into the term, as in groups of elders gathering together and officially ratifying this or that as binding dogma. Later rabbinic literature does paint things in that way, but whether the portrait which the later Talmud paints is actually historical fact is now something that is uncertain.
All the sources tell us is this: before Jerusalem fell, Rabbi Johanan ben-Zakkai established an academy at Yavneh (Jamnia) which proceeded to function like a Sanhedrin between the period between the Jewish revolts of AD 70-132. He was then succeeded by Rabbi Gamaliel II. Somewhere between AD 80 and AD 117 Gamaliel was deposed for a time, during which Eleazar ben-Azariah was installed as head of the academy. According to the Mishnah, at the day of Eleazar’s installation, the sages ruled that both Song of Songs and Ecclesiastes “make the hands unclean” (i.e. are holy). The same passage goes on to state that “all the Holy Scriptures render the hands unclean,” and so it is clear that the point at issue was whether the two books ranked among the Scriptures. This passage is then followed by a series of enactments introduced by the phrase “on that day” (Mishnah,
Yadaim 3.5-4.4). Later tradition (Talmud,
Berakhoth 28a), taking this formula at face value, claimed that every ruling prefixed by the phrase were indeed made on the same occasion.
Now as mentioned, applying the Christian idea of what a ‘council’ is to these debates is probably off. On the contrary, the deliberations at Yavneh were closer to the character of a school, academy, or court. All that this anecdote tells us was that there was some debate about the exact status of these two books, not that the canon of Scripture was being officially decided . In fact, it would seem that the dispute were not terminated by the decisions at Yavneh: even as late as the late 2nd century, Rabbi Meir (circa 135-170), famous as one of the greatest of the Tannaim of the fourth generation, was disputing the idea that Ecclesiastes defiled the hands. There is no evidence that the status of other Writings was debated, or that a final decision was reached. In any case, it is even doubtful whether the actions of the academy were official decisions; there was probably no body in Judaism that functioned in an ‘official’ capacity post-AD 70.