Very interesting chapter with challenges in interpretation. In my view the best interpretation is to see this as Jesus preparing the Jews for the Gospel which will soon be known and that after he dies and is resurrected the Jews will need to see him as Savior and Lord or they will miss out on heaven. Sometimes you almost wish Matthew or Jesus in this case wouid stop and explain the gospel within the text of the chapter but they don't because the era of the Gospel is not yet in existence. Jesus has yet to die for the sin of mankind and rise from the dead. Jesus is giving them the warning now. Fortunately, man Jews, at Pentecost and in the early formation of the church did come to see Jesus as Savior and Lord. Perhaps they did remember these teachings and come under conviction for them.
Acts 2:22-41 (LSB) 22 “Men of Israel, listen to these words: Jesus the Nazarene, a man attested to you by God with miracles and wonders and signs which God did through Him in your midst, just as you yourselves know-- 23 this Man, delivered over by the predetermined plan and foreknowledge of God, you nailed to a cross by the hands of lawless men and put Him to death. 24 “But God raised Him up again, putting an end to the agony of death, since it was impossible for Him to be held in its power. 25 “For David says of Him, ‘I SAW THE LORD CONTINUALLY BEFORE ME; BECAUSE HE IS AT MY RIGHT HAND, SO THAT I WILL NOT BE SHAKEN. 26 ‘THEREFORE MY HEART WAS GLAD AND MY TONGUE EXULTED; MOREOVER MY FLESH ALSO WILL LIVE IN HOPE; 27 BECAUSE YOU WILL NOT FORSAKE MY SOUL TO HADES, NOR GIVE YOUR HOLY ONE OVER TO SEE CORRUPTION. 28 ‘YOU HAVE MADE KNOWN TO ME THE WAYS OF LIFE; YOU WILL MAKE ME FULL OF GLADNESS WITH YOUR PRESENCE.’ 29 “Men, brothers, I may confidently say to you regarding the patriarch David that he both died and was buried, and his tomb is with us to this day. 30 “And so, because he was a prophet and knew that GOD HAD SWORN TO HIM WITH AN OATH TO SET one OF THE FRUIT OF HIS BODY ON HIS THRONE, 31 he looked ahead and spoke of the resurrection of the Christ, that HE WAS NEITHER FORSAKEN TO HADES, NOR DID His flesh SEE CORRUPTION. 32 “This Jesus God raised up again, to which we are all witnesses. 33 “Therefore having been exalted to the right hand of God, and having received from the Father the promise of the Holy Spirit, He has poured out this which you both see and hear. 34 “For David did not ascend into the heavens, but he himself says: ‘THE LORD SAID TO MY LORD, “SIT AT MY RIGHT HAND, 35 UNTIL I PUT YOUR ENEMIES AS A FOOTSTOOL FOR YOUR FEET.”’ 36 “Therefore let all the house of Israel know for certain that God has made Him both Lord and Christ--this Jesus whom you crucified.” 37 Now when they heard this, they were pierced to the heart, and said to Peter and the rest of the apostles, “Men, brothers, what should we do?” 38 And Peter said to them, “Repent, and each of you be baptized in the name of Jesus Christ for the forgiveness of your sins; and you will receive the gift of the Holy Spirit. 39 “For the promise is for you and your children and for all who are far off, as many as the Lord our God will call to Himself.” 40 And with many other words he solemnly bore witness and kept on exhorting them, saying, “Be saved from this crooked generation!” 41 So then, those who had received his word were baptized; and that day there were added about three thousand souls.