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The people with Cornelius knew about Jesus but that doesn’t mean they yet believed in Him. While Peter preaches to them, they become convinced and the Holy Spirit descends on them. This is a second Pentecost and in one way is even greater than the first for it shows that the Gentiles are invited by Christ as well. And then they are baptized. And? At other times, people have faith and are baptized for some time and only later receive a greater gift of the Holy Spirit (Acts 8:16-17). And?

You are correct that Cornelius was not yet saved before Peter preached to them and they believed. And what they believe was

To him give all the prophets witness, that through his name whosoever believeth in him shall receive remission of sins. (Acts 10:43)

That was it, and indeed they did believe, with God giving "them the Holy Ghost, even as he did unto us; And put no difference between us and them, purifying their hearts by faith. (Acts 15:8-9)

The same gift promised to those in Acts 2:38 if they would repent and believe in the LJC was essentially promised to those in Acts 10:43 (not by works..by the "washing of regeneration": Titus 3:5)

However, there is no contradiction, and need to attribute a unique condition of heart to Cornelius and company if we understand both as a call to faith, this being what purifies the heart. Since real faith effects confession, and if one confesses the Lord Jesus from the heart then it means one believes, then the promises is made "Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost. (Acts 2:38)

That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved. For with the heart man believeth unto righteousness; and with the mouth confession is made unto salvation. For the scripture saith, Whosoever believeth on him shall not be ashamed. (Romans 10:9-11)

It is only such faith that will confess the Lord Jesus, which baptism formally does, that is salvific, But since it is actually the faith behind the work that justifies, that appropriates the purifying their hearts, the "washing of regeneration," then the promise can be made, "To him give all the prophets witness, that through his name whosoever believeth in him shall receive remission of sins." (Acts 10:43) And which was realized.

Such souls are washed, sanctified, and "justified justified in the name of the Lord Jesus, and by the Spirit of our God." (1 Corinthians 6:11) And thus ojn Christ's account such are accepted in the Beloved and made to sit together with Him in Heaven, (Eph. 1:6; 2:6) which will be realized when they die in overcoming, saving faith, (Rv. 3:21) or at His return. (1Ths. 4:17)

However, it cannot be the confession that merits justification, since it is faith which is counted for righteousness, (Rm. 4:5) nor that the change that regeneration effects makes them good enough to be with God, unless simply being forgiven is enough and thus maintaining a sinless state, versus perfection of character also being required, which even Paul confessed he lacked, and strove to be in this life as much as a resurrected believer will be, which event he looked forward to as being what would finally deal with his "vile body," (Phil 3:8-21) though to be presently absent from the body was to be present with the Lord. (2 Corinthians 5:8; Phil 1:21-22)

As for Acts 8:16-17, I in the absence of more persuasion, I also hold to be reasonable what you conclude, that "At other times [though to be precise, this was the only time recorded], people have faith and are baptized for some time and only later receive a greater gift of the Holy Spirit .

Some posit that the apostles were required to lay hands on such, but the Ethiopian eunuch was baptized by deacon Phillip and went on his way joyfully without any.

Paul for his part believed enough to obey God/Christ (which he though he was doing before) but awaited further revelation before he was filled with the Spirit, which was provided thru "a certain disciple at Damascus," (Acts 9:10) "one Ananias, a devout man according to the law," who confirms Christ as being "that Just One" whom he was to serve, and instructs "be baptized, and wash away thy sins, calling on the name of the Lord," (Acts 22:10-16) thus confessing the Lord.

Yet based on the two but supplementary accounts, before he was baptized Ananias "entered into the house; and putting his hands on him said, Brother Saul, the Lord, even Jesus, that appeared unto thee in the way as thou camest, hath sent me, that thou mightest receive thy sight, and be filled with the Holy Ghost. And immediately there fell from his eyes as it had been scales: and he received sight forthwith, and arose, and was baptized. (Acts 9:17-18)

It is certain that God cannot be put in a box, but it is evident that baptism and conversion were normatively one event in Scripture, since faith in the heart and confession with the lips - and legs via baptism - go hands in hand, and one cannot claim to believe while not obeying.

Yet again, it is faith which appropriates justification with the purifying of the heart, faith being counted as righteousness, even before it is expressed in baptism, which countless examples of conversions with profound changes in heart and life via regeneration testify to, as with Cornelius and company, though the time of expression be the time when one effectually believes. That is my conclusion without any constraints over where the evidences leads to.