Peter referred to the Great Commission, which Jesus gave his disciples after His resurrection ( Acts 10:41), in Acts 10:42. [source][source][source]
"This entire experience is an illustration of the commission of Matthew 28:19-20. Peter went where God sent him and made disciples ("teach") of the Gentiles. Then he baptized them and taught them the Word." [1][source]
Jesus Christ will one day judge all people as forgiven or not forgiven (cf. Acts 17:31). To be forgiven one must "believe in Him" (cf. Acts 5:14; Acts 9:42; Acts 11:17). Peter said this is what the Old Testament prophets taught (e.g, Isaiah 53:11; Jeremiah 31:34; Ezekiel 36:25-26; et al.). The Messiah (Christ) would be the Judge of all people, and Jesus of Nazareth is that Messiah (cf. John 5:27). The Lord of all ( Acts 10:36) is also the Judge of all ( Acts 10:42). [source][source][source]
Note how Peter stressed the universal benefit of Jesus" ministry in this message to Gentiles; it was for Gentiles as well as Jews. Not only is Jesus Lord of all ( Acts 10:36), but He went about healing all ( Acts 10:38). Furthermore He is the Judge of all ( Acts 10:42) to whom all the prophets bore witness ( Acts 10:43 a), and God forgives all who believe in Him ( Acts 10:43 b). [source][source][source]
"This simple outline [2] . . . is perhaps the clearest NT example of the kerygma, the earliest form in which the apostolic proclamation of the gospel was apparently couched." [3][source]