"I would suggest the sinner has submitted to the will of Christ long before he/she is baptized. Otherwise they wouldn't want to be baptized. Baptism is an outward manifestation of that submission."
Please show me Biblical proof that baptism is an outward manifestation of the submission to Christ. Without Biblical proof, this is just your opinion.
In Him, you also, after listening to the message of truth, the gospel of your salvation-having also believed, you were sealed in Him with the Holy Spirit of promise. Eph 1:13
Cornelius and company received the gift of the Holy Spirit BEFORE they were baptized. As we can see from Ephesians the Holy Spirit is our guarantee of our promise-not our baptism.
BTW-Some of the words Peter spoke were:
Of Him all the prophets bear witness that through His name everyone who believes in Him receives forgiveness of sins. Acts 10:43
No mention of baptism.