God is no respecter of person – salvation is the same for Jew and Gentile under the NT. Peter was instructed to speak unto Cornelius "words whereby he would be saved" (Acts 11:14) because "faith comes by hearing" and those words preached by Peter included the command to be baptized in water.
And [Peter] commanded [Cornelius and his house] to be baptized in the name of the Lord. Then they asked him to stay a few days. (Acts 10:48 (NKJV)
Cornelius, like Paul was commanded to “be baptized†to wash away his sin.
And now why tarriest thou? arise, and be baptized, and wash away thy sins, calling on the name of the Lord.
(Act 22:16 KJV)
The pattern is believe and be baptized and then comes salvation. The Bible does not say ‘believe and be saved and then be baptized’.
He that believeth and is baptized shall be saved
(Mar 16:16 KJV)