After the Shulchan Aruch was put together by the Beis Yosef and then following that with the glosses of the Rema, when did this sefer became "accepted" as the basis for deciding halachic matters in all of the Jewish people (as opposed to the Tur, Rambam, any other halachic sefer or learning through the Gemara and paskening.) While I realize achronim that came afterwards wrote commentaries on the Shulchan Aruch and Rema and even sometimes argued. But more or less this became the sefer that is the starting point for halacha. When did this happen on a large scale and who was/were the person/people that decided that this would be the sefer for everyone to follow.
Sometimes it's not really possible to give an exact answer as to why certain books become the standard. For example, i don't think anyone would have predicted that nearly a thousand years after the Rambam that the only community that still followed him would be the Yemenites. You would have figured the community of Cairo would have been the one to hold his Torch, but sometimes history happens and things change in unpredictable ways.
It is my opinion that there are a few historical coincidences that caused the Shulchan Arukh to spread as much as it did, and cause it to become a sort of standard up until even today.
The biggest influence was undoubtedly the expulsion of Jews from Spain in 1492. Not only was Yosef Caro one of the expulsed, but thousands of his comrades were scattered all over the world. And not only were these Sephardim entering new lands in vast numbers, they were not integrating into their new communities. Rather than change minhags to the new lands they found themselves in as was normative halacha, they decided to open up their own Synagogues, or to continue their practices despite the prevailing customs. And so when Yosef Caro wrote his great work the Shulchan Arukh, being a Sephardic work meant for Sephardic Jews, the book quickly spread all over the world, to all the communities where Sephardim had landed. Caro had an idea that his work might be problematic, and therefore included the following words in his intro to the Bet Yosef
“And if there are countries which hold that certain things are prohibited, even if we rule differently, they should continue to uphold their custom, as they already accepted upon themselves the words of the sage who prohibited it, and they may not be lenient in the matter as the Talmud states in Pesahim (51B)”
But despite these concerns, the Sephardim in their new lands were not only holding to Caro despite the prevailing custom, these Sephardim were also trying to bully other communities into following the Shulchan Arukh. This bullying went so far that Yosef Caro himself had to respond to this in one of his teshuvoth.
Rabbi Yosef Karo (author of שולחן ערוך):
"Who is he whose heart conspires to approach forcing congregations who practice according to the RaMBáM of blessed memory, to go by any one of the early or latter-day Torah authorities?!
... Is it not a case of a fortiori, that regarding the School of Shammai—that the halakháh does not go according to them—they [the Talmudic Sages] said ‘if [one practices] like the School of Shammai [he may do so, but] according to their leniencies and their stringencies’: The RaMBáM, is the greatest of all the Toráh authorities, and all the communities of the Land of Israel and the Arab-controlled lands and the West [North Africa] practice according to his word, and accepted him upon themselves as their Chief Rabbi. Whoever practices according to him [the RaMbáM] with his leniencies and his stringencies, why coerce them to budge from him?
And all the more so if also their fathers and forefathers practiced accordingly: for their children are not to turn right or left from the RaMBaM of blessed memory. And even if communities that practice according to the Rosh or other authorities like him became the majority, they cannot coerce the minority of congregations practicing according to the RaMBaM of blessed memory, to practice like they do. And there is no issue here concerning the prohibition against having two courts in the same city [‘lo tithgodedu’], since every congregation should practice according to its original custom…”
So we see that in Yosef Caro's lifetime there was an attempt to force congregations to follow him, despite the Rambam being the normative standard for Jews in Arab lands. But we in the modern era cannot fathom the amount of Sephardic Jews that would enter into new communities, sometimes they arrived in such populations that they outnumbered the indigenous communities. So if the normative minhag was x by a population of 500, but now there's a new minhag from a new populace of 3,000, something is bound to change.
The other reason why the Shulchan Arukh became the standard was because the mindset of the observant Jew was changing. The earlier halachic authors (such as the Rambam) had a mindset (which was shared by the general populus) that there was one right/correct way to practice halachah, and that even if there were contrary opinions, you would have no need to worry about them since you are following the correct path. For the Rambam (and older halachic authors) if the majority of opinions said x, but they felt that y was correct, they would have no issue saying the correct halacha is y. While they might value and consider contrary opinions, they were not things that one needed to be concerned with. There wasn't the same amount of "weight" of majority of opinions. The truth was the truth, whether 1 person said it, or 1,000 people. If the Rambam said x, then you could do x without any need to worry about any other contradictory opinions. The Rambam felt that he had the authority and opinion to give new rulings, even if no one had ruled that way before. But as time went on, a new situation started to arise: if the Rambam said X, the Rosh said Y, and the Tur said Z, then people started to doubt what the correct option was as many of these opinions were mutually exclusive. Because if you follow the Rambams X, then you would be going against the Rosh and the Tur who had different opinions. So there became the new option of [XYZ], a combination or comparison of these different opinions, and people would try to fulfill all three, or side with a majority. If the Rambam says that the correct way to pray was to prostrate on the ground, but there are now 5 halachic authorities who go against this, then this new mindset would say that clearly the more correct way to pray is to follow the majority of the opinions. Yosef Caros work was the beginning of this process as he would compare the 3 main opinions and would [often] side with the majority. Whereas the Rambam would not rule based by majority, he would rule based on correctness. And one wouldn't need to worry what other opinions were, nor feel any pressure to follow them.
So those are the two situations that caused the work to become as influential as it did. And within 200 years of its authoring, it became the standard for most Jewish communities. And we still see this change in following opinions panning out in today's generations, where "minority" opinions aren't as valid as "majority" opinions that agree.