Notice that it does not say that those who believed were given eternal life. Rather, it says that it was those who had been appointed to eternal life who then believed what Paul and Barnabas said. They had already been appointed to eternal life, and that appointment included the faith to hear and accept the message. The appointment came first, and the gift of faith followed. That is how God’s calling works. It is entirely outside of our control.
Now, this incident does not tell us how far in advance God appointed some of the Gentiles there to eternal life. If we believe what it says in Ephesians 1:4, it was before the foundation of the world. But let’s go to another witness of Scripture that makes this even more clear: