Really?
If you are Catholic , I will ask if the infants have properly "believed "before they are baptized?
If you are COC if a man that came foreword in faith and repented and believed drops dead before his baptism ...does he burn in hell?
Here is the gospel that Paul preached
1Cr 15:1 Moreover, brethren, I declare unto you the gospel which I preached unto you, which also ye have received, and wherein ye stand;
1Cr 15:2 By which also ye are saved, if ye keep in memory what I preached unto you, unless ye have believed in vain.
1Cr 15:3 For I delivered unto you first of all that which I also received, how that Christ died for our sins according to the scriptures;
1Cr 15:4 And that he was buried, and that he rose again the third day according to the scriptures:
Not one word about Baptism in the gospel that saves .
Read the words of Paul
1Cr 1:13 Is Christ divided? was Paul crucified for you? or were ye baptized in the name of Paul?
1Cr 1:14 I thank God that I baptized none of you, but Crispus and Gaius;
1Cr 1:15 Lest any should say that I had baptized in mine own name.
1Cr 1:16 And I baptized also the household of Stephanas: besides, I know not whether I baptized any other.
1Cr 1:17 For Christ sent me not to baptize, but to preach the gospel: not with wisdom of words, lest the cross of Christ should be made of none effect.
1Cr 1:18 For the preaching of the cross is to them that perish foolishness; but unto us which are saved it is the power of God.
First of all, the practice of infant baptism has no foundation in Scripture. Second, using "hard cases" such as a person dying right before baptism is grasping at straws. God is just and He has the final say on who is saved. However, we on this earth only have the Bible record to show us what He commands of us in order to receive salvation.
Regarding 1 Corinthians, Paul is speaking to members of the church at Corinth. These people are saved. In the first few verses you quoted, no, he does not specifically talk about baptism. But he does refer to the Gospel that he did preach to them. In Acts 18, we see Paul preaching to those in Corinth. In verse 8, it says "and many of the Corinthians hearing believed, and were baptized". If baptism isn't a part of the Gospel, then how did they know to be baptized?
As you noted, he does talk about baptism later in the same chapter. However, Paul is not saying baptism is not a part of the Gospel. You even included verse 13 which shows he is talking about those in Corinth who were claiming the name of the one who baptized them, not the name of Christ. His problem was not with baptism, but with claiming the name of the baptizer.