The hand of God was ALWAYS at work in the hearts of believers to recognize, through the Holy Spirit, what writings were Divinely-inspired. If you read in Deuteronomy 18, the Lord gave His people a hard and fast guideline to know what came directly from Him to His chosen Prophets and what was not from Him. He told them:
The Lord said to me: “What they say is good. I will raise up for them a prophet like you from among their fellow Israelites, and I will put my words in his mouth. He will tell them everything I command him. I myself will call to account anyone who does not listen to my words that the prophet speaks in my name. But a prophet who presumes to speak in my name anything I have not commanded, or a prophet who speaks in the name of other gods, is to be put to death.” You may say to yourselves, “How can we know when a message has not been spoken by the Lord?” If what a prophet proclaims in the name of the Lord does not take place or come true, that is a message the Lord has not spoken. That prophet has spoken presumptuously, so do not be alarmed. (Deut. 18:17-22)
Have all the Mormon "prophets" passed the test of the Lord? Has everything they prophesied to come to pass actually happened exactly as they said it would?
But, getting back to your question, the Jews received the writings from the Prophets of the Lord and obeyed God's commands. There was a "canon" of the Scriptures that make up the Old Testament recognized by the Jewish religious community and those books that comprise the New Testament were also recognized by the early Christians as from the Lord just as they did for the Old Testament. The early church's recognition of them is not what made them sacred Scripture, they were God-breathed whether or not anyone received them. God DID lead His sheep to recognize His voice through these writings and we still do, even after all this time.