Did every Jew have to believe in Jesus as the Christ?
Yes. The context states that every Jew had to believe, be converted, and understand that Jesus was the Christ. Peter, speaking to Israel as the covenant people, urged them to accept Him as King and Messiah so God would send Him to bless them in turning away.
Les explains that Peter addresses Israel as the children of the prophets and the children of the covenant God made with their fathers, saying to Abraham, “and in thy seed shall all the kindreds of the earth be blessed.” That seed of Abraham goes back to Genesis 3:15, the seed of the woman, and the seed is the Christ. This was part of God’s plan of redemption for the whole human race, but it would come through the nation of Israel. Peter pleads with them as the covenant people: believe it, accept Him as King and Messiah, and God would yet send Him. Then verse 26 says, “Unto you first,” God, having raised up His Son Jesus, sent Him to bless you in turning away. Les points out that every one had to believe and be converted and understand that Jesus was the Christ. Had they done so, they could have had the Tribulation, the King, and the Kingdom just that quick, and then evangelized the whole Gentile world as the Old Testament prophesied.
Ye are the children of the prophets, and of the covenant which God made with our fathers, saying unto Abraham, And in thy seed shall all the kindreds of the earth be blessed.
Unto you first God, having raised up his Son Jesus, sent him to bless you, in turning away every one of you from his iniquities.