The Gedolim, including the Shach, shortly after it was written accepted it as binding. This is the same thing that happened when Klal Yisroel decided that the period of Chazal has ended after the 7th generation of Amorayim (Mar Zutra, Mar bar Rav Ashi, etc), and nobody from here on in can add to the Gemora. There was no “halachah lmoshe misinai” that told us that the Gemora was sealed; it was the accepted reality told to us by our Gedolim. The same thing applies to accepting the Shulchan Aruch and Rema.
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