Why was Israel in a position to accept their king at the time of Acts 3?
Israel was positioned to accept their king because the atoning work was finished, Jesus had been raised from the dead, and He had ascended to sit at God's right hand according to Psalms 110:1, ready to return. As children of the prophets and covenant, they needed only to believe.
Les explains that Peter addressed the Jews as children of the prophets and of the covenant God made with Abraham, saying, 'In thy seed shall all the kindreds of the earth be blessed.' God raised up His Son Jesus and sent Him to bless them by turning every one of them from their iniquities. God had it in mind that Israel was now in a position to accept their king: the atoning work was made, Jesus was raised from the dead, and He had ascended according to Psalms 110:1 to sit at God's right hand until His enemies are made His footstool. He was ready to come back if Israel would just believe it. Les also stresses that God made valid offers knowing they would not be accepted, such as to Adam and Eve and at Kadesh Barnea.
The LORD said unto my Lord, Sit thou at my right hand, until I make thine enemies thy footstool.