Paul's question presupposes that one receives the Holy Spirit at the same time he or she believes the gospel. It should also be noted that a person receives the Spirit upon getting saved (Romans 8:9; 1 Corinthians 12:13; Ephesians 1:13-14; Galatians 3:2). The two events are not separated in Scripture.
Scripture distinguishes between faith and baptism (Acts 18:8). Moreover, Acts 19:1-7 does not make mention of any works that can get us right with God. Faith is the object of emphasis. Thus, baptism cannot be a requirement in order to be justified before God.