The book of Acts has a number of terms to describe people who followed Judaism to a degree and would become followers of Christ. Their descriptions make them sound like believers who naturally accepted Christ when they heard of what He did for them, but this was not necessarily the case. These terms include proselytes, devout, worshipers of God, and those who feared God.
Proselytes (prosēlytos) included those who heard the mighty works of God in their own tongues (Acts 2:11), Nicolaus from Antioch (Acts 6:5), and synagogue-attending converts who followed Paul and Barnabas (Acts 13:43). For the latter, they were even described as devout proselytes (sebō prosēlytos; Acts 13:43). Being a proselyte could describe one’s present (Acts 2:11) or past (Acts 6:5) adherence to Judaism.
Those who were devout (sebō) or worshipers of God (sebō theos) included those who would believe the gospel, such as the devout proselytes in Pisidian Antioch (13:43), Lydia (Acts 16:14), devout Greeks in Berea (Acts 17:4), devout Athenians who attended the synagogue (Acts 17:17), and Titius Justus who housed Paul (Acts 18:7). There is one instance in which the devout were synagogue adherents but persecuted Paul and Barnabas (Acts 13:50). So, a devout person might apparently deny the gospel, indicating an absence of faith to begin with. This being the case, whether or not those who believed in Christ had faith prior to hearing the gospel is hard to say. What we do know is that, for some of them, their time in the synagogue prepared them to accept the Messiah (e.g., Lydia). For others, however, it did not (Acts 13:50).
Another term for devout (eusebēs) describes Cornelius and one of his soldiers (Acts 10:2, 7). Cornelius was also one who feared God (or, a “God-fearer”; phobeō theos; Acts 10:2, 22), as were Paul’s non-Jewish listeners in Pisidian Antioch (Acts 13:16, 26). In these instances, Cornelius would believe the gospel, and Paul’s God-fearing listeners would follow his gospel. As with the devout and worshipers of God, whether or not these individuals had faith prior to accepting the gospel is hard to say. For instance, Cornelius is described as devout, upright, fearing God, a giver of alms, and eagerly obeying the angel that told him to send for Peter (Acts 10:2–8, 22). At the same time, before believing the gospel, he had been considered unclean by Peter and the Jews (Acts 10:28; 11:3), likely because he had not fully converted to Judaism. He probably followed the OT in many ways but had not been circumcised (Acts 11:3; cf. Exodus 12:48). This being the case, though fearing God to a degree and being slowly but effectually drawn to saving faith over time, he needed to hear the Word of God about Jesus Christ, be granted by God the repentance that leads to life, and believe this message in order to be saved (Acts 10:34; 11:1, 14, 18).