This question requires a “yes and no” answer. The no aspect of the answer comes because for many Jews who heard the claims of Christianity this fulfilled the promises they had grown up believing. Jews have always understood their ancestors were chosen to have a unique relationship with God and that they today carry on that relationship. So for many Jews who claim to believe in Jesus as Messiah, they would have identified a truth promised to them and accepted it. This is not to say that they did not see a change in relationship with God. The story of the moving of the Holy Spirit in Acts 2 is designed to help us understand that the disciples understood their relationship with God to be altered through the power of Jesus. The strange symbolism of “tongues of fire” and “rushing wind” is to help us understand that this community was God’s new temple. Yet, it is not as if one day they did not have a relationship with God and the next they did; rather, this was a turning point for them into a new expression of that relationship. Perhaps (but don’t hold me to this part) the best analogy is that of an engaged couple being married, in one sense the relationship alters on the day of the wedding but in another sense, it continues on just as it did the day before. In this sense Jews and Christians both see worship as entering into and continuing a relationship with God. I should also point out that the one major difference in the way Jews and Christians perceived the relationship with God is “nearness”. Jews looked on human impurity as preventing us from getting too close to God, thus depending on how ritually pure you were you had varying places in the Temple (God’s home) which you could enter. Christians understand Jesus’ purity transmits to us in a very real way making us pure and able to enter God’s presence.
This is different for Greco-Romans who would have come out of pagan religions. In these cases, certainly a case can be made that they would have been drawn to an actual relationship with God. The gods of pagan cultures were described (even by worshipers) as capricious, selfish, aloof, unconcerned, random, and unpredictable. To be presented with a God which was none of those things and cared about humanity and justice certainly must have been a draw to some who valued a caring God.
Leon Morris The Apostolic Preaching of the Cross
Scot McKnight The Jesus Creed