The Lord Jesus Christ ascribed inspired authority to the O.T. Scriptures (Matthew 5:18; 15:3; Mark 12:6; John 10:35). He also promised His chosen servants that after His return to heaven, He would send the Holy Spirit to remind them of the teaching He had given them and to communicate further truth to them. (John 14:26; cf. John 16:12-13).
In His ministry, the Lord Jesus, as has been shown in the O.P., attacked the Jewish authorities for exalting their traditions at the expense of Scripture (Mark 7:7ff). He also constantly referred them to the Scriptures. 'Have you not read.......?' (cf. Matthew 12:3-5; 19:4; 21:16; 22:31; Mark 2:25; 12:10, 16; 13:14; Luke 6:3; 10:26). For Him, the Scriptures were not the supreme authority but the only authority.
Recent discoveries of fragments of Matthew and Mark mean that those Gospels were probably written by AD 50, and almost everything else by AD 70 (possibly excluding John's letters and Revelation).
The N.T. Scriptures were immediately accepted as being the word of God. Paul quotes Luke 10:7 alongside Deut. 25:4 (1 Timothy 5:18), and Peter endorses Paul's letters in 1 Peter 3:15-16. The ECFs quote extensively from the N.T. showing that they regarded them as authoritative. For example, somewhere around AD 95, Clement of Rome wrote: 'Take up the epistle of the blessed Apostle Paul. What did he write to you at the time when the Gospel first began to be preached? Truly, under the inspiration of the Holy Spirit, he wrote to you concerning himself and Cephas and Apollos.....' Clement did not wait for any authority to tell him that 1 Corinthians was inspired Scripture. Clement also quoted from Psalm 118:18 and Hebrews 12:6 and described them both as the 'Holy Word.'
Polycarp, in his letter to the church at Philippi, quotes from Matthew, Luke, Acts, Romans, 1 Cor., Gal., Eph., Phil., 2 Thes., 1 & 2 Tim., and Hebrews. He quotes 1 Peter so often and widely that Bruce Metzger suggests that he must have known it practically by heart. He introduces quotations by saying, "Remember what the Lord said in His teaching....." and "As the Lord said......" He also wrote, " I trust you are well versed in the sacred Scriptures and that nothing is hid from you." He assumed that his readers also has access to the N.T. Polycarp died in AD 155, long before the Roman Catholic Church reared its head.
Which ones? There were plenty of false writings floating around that were claimed to be inspired of God and it took the One Universal Christian Church and those who had authority to finally whittle them down to the writings that were ultimately accepted to be the NT Canon. You seem to believe that Scriptures you now hold in your hands were the only ones available at that time and such a thing is just not true.