The Bible doesn’t tell us how Joel, Amos, Micah, Zephaniah, Habakkuk, Malachi, etc. proved themselves as prophets in the eyes of their contemporaries. Their alleged prophecies were fulfilled, according to the NT authors. Before then, what was their status?

This is a good question.  The answer is that we do not have access to the relevant information of who these books came to be canonized, and how these particular prophets came to be accepted as true prophets of YHWH.  We do have a record in the Pentateuch of the qualifications for one to be considered a prophet.  This is found in Deuteronomy 18:22.  Here, God tells his people that, “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.”  We have a relatively small number of examples of biblical prophets for whom we know their short-term predictions came true. A good example is Ezekiel 33:21-22.  I have not done a careful study of this, but I would guess that we have such biblical evidence for less than half of the recorded canonical prophets.  But, lack of evidence is not evidence of lack.  Just because we do not have these successful predictions recorded in the actual canonical writings of Micah or Amos does not mean that such evidence did not exist in their lifetimes. Can we assume that, in his lifetime, Amos was put to this test and passed the test?  Maybe.  Probably.  But this is speculation, and we will be wise to remain silent on things we do not have information available to us.

Here is what we know for sure.  The six prophets you mentioned were included in the Hebrew/Jewish canon of Scripture well before the time of Christ.  Josephus mentions them in the late first century. All of them are found in at least partial manuscript in the Dead Sea Scrolls.  All of them are in the Jewish Greek translation known as the Septuagint, and all of them are quoted in the New Testament, used as Scripture. So, exactly why the Jews considered Habakkuk, Zephaniah, etc. to be canonical we may not be sure. But we can be sure that the Jews as a whole accepted them as prophets.  In the Jewish Targums, Mishnah and/or Talmud we can probably find some material from Jewish sources on the inspiration of Amos or Micah, but, to be honest, I am no expert on these materials, and I am not aware of any evidence of the sort you are looking for—comments of their contemporaries.

By the way, I am not sure why you call these “alleged” prophecies. Micah 5:2, Joel 2:28-32, Amos 9:11-13, and Malachi 4:5-6 are not “alleged” prophecies, and they were certainly fulfilled in Christ and in his kingdom.

John Oakes