It is interesting that most English translations use the word "scriptures" which may seem somewhat ambiguous. However, Young's uses specifically "Writings".
" for I delivered to you first, what also I did receive, that Christ died for our sins, according to the Writings,
4 and that he was buried, and that he hath risen on the third day, according to the Writings," (YLT)
The Hebrews referred to the three sections of the OT as the Tor'ah, or the Teaching (also called the Pentateuch - the five books of Moses); the Nevi'im (Prophets); and the Ketuvim (Writings). In shorthand the TNK, or Tanakh.
"The last of the three divisions, the Ketuvim, contains poetry (devotional and erotic), theology, and drama in Psalms, Proverbs, Job, Song of Songs (attributed to King Solomon), Ruth, Lamentations, Ecclesiastes, Esther, Daniel, Ezra-Nehemiah, and Chronicles." Source: here
Did Paul only mean the Ketuvim (Writings) or was it all OT Messianic prophesy? Most conclude that all OT scripture prophesy of the death and resurrection of Christ is included.
Excerpt from Benson Commentary:
"According to the Scriptures — The Scriptures which foretold the resurrection of Christ on the third day, and to which St. Paul refers, are Psalm 16:10, (which Peter, Acts 2:31, expressly affirmed to be a prediction of that event,) and Jonah 1:17, which our Lord himself affirmed to be a typical prophecy of his continuing three days in the heart of the earth, and of his subsequent resurrection. " Source: here
Excerpt from Gill's Exposition of the Entire Bible:
"how that Christ died for our sins according to the Scriptures; that is, of the Old Testament, the writings of Moses, and the prophets, according to Scripture promises, Scripture types, and Scripture prophecies; particularly Genesis 3:15 Daniel 9:24 which declare that his heel was to be bruised, that he should be brought to the dust of death, should pour out his soul unto death, and be stricken and cut off in a judicial way, and that for sins; not his own, but for the sins of his people, in order to atone for them, procure the pardon of them, take them away, make an end of them, and abolish them; all which he has done, as the Gospel declares, and the apostle affirms; and thereby was accomplished what Moses and the prophets did say should come to pass. Every promise, type, and prophecy recorded in the law, in the prophets, and in the psalms, concerning his sufferings and death, had their fulfilment in him; nothing was more clearly prefigured and foretold, and nothing more punctually and fully answered. " Source: Ibid.
1 Corinthians is held to have been written approx. 55 AD before the Passover. As this predates even the gospels, it would appear that the NT scriptures cannot be in view here, as they would not have been circulated before this letter to the Corinthians. Therefore the "Scriptures" must refer to the OT prophesies.
See Dating the New Testament here