If you carefully read the writings of the New Testament, it is clear that the scriptures being referred to were the Jewish Bible or Hebrew Tanach. Those awaiting the messiah were initially Jews that believed the Jewish Bible (what Christians refer to as the Old Testament) was the word of God and they were well versed in it. They went to the synagogues on the Sabbath to hear it read. They studied it and discussed it often as part of their culture.
The New Testament writers also quoted or alluded to other books that they may have considered as scripture. According to Wikipedia, these other books quoted or alluded to include the following:
1. Book of Enoch (Jude 4,6,13,14-15, 2 Peter 2:4;3:13)
2. Life of Adam and Eve (2 Corinthians 11:14 "Satan as an angel of light", 12:2 "Third Heaven")
3. Assumption of Moses (Jude 9 "Michael… body of Moses")
4. Martyrdom of Isaiah (Hebrews 11:37 "they were sawn in two")
Of these 4 books referenced, the Book of Enoch was the one most likely considered scripture by the early church as it has been found among the Dead Sea Scrolls and was quoted multiple times in both Jude and 2 Peter. It wasn’t canonized by the church and may or may not be scripture. However, the Book of Enoch has a lot of writing related to the messiah as well as information on the angelic realm and is well worth reading for those that have never read it.
Orthodox Jews have an annual reading and study cycle of the first 5 books of the Bible referred to as the Torah. They consider this text as special since it was direct revelation from God to the Israelites on Mt. Sinai. The remainder of the Jewish Bible is also considered to be the word of God by indirect revelation through various writers. However, Jews place a special emphasis on studying the Torah because it is direct revelation from God. It is the Torah and other books of the Jewish Bible that are referred to as the Scriptures in the Christian New Testament. Know the scriptures and study them well.