I don't wish to sound "mean spirited". However, I have had a number of people in my life tell me you must be baptized to be saved. That is, quite frankly, hogwash. (no pun intended) That is not to minimize the importance of baptism but only to emphasize the total regeneration process.
The Bible list baptism before salvation in several of the verses because it was an important sacrament of the church and is a method to declare youself as a believer. But as I've illustrated with Cornelius, it is the filling of the Holy Spirit which saves you and this come before baptism. You are filled with the Holy Spirit the moment God regenerates you.
In Acts 2:38, Peter tells those at Pentecost that you will be given the gift of the Holy Spirit after you repent and are baptized. Cornelius received the Holy Spirit as a sign to the Jewish Christians that Gentiles could be saved as well. There are only two instances where the Holy Spirit manifests itself as it did with Cornelius, the other being when the apostles spoke at Pentecost. However, in all other conversion accounts in Acts, including Cornelius, baptism is mentioned.
I have a question I would like for you to answer. Can you be saved before you have your sins removed?