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I seriously doubt that because there is nothing in the New Testament that shows that any of the Apostles thought so or acted as if he was the "key" person.

Gal. 1, where St. Paul visits St. Peter:

You see his humble soul? You see how he sets himself below all saints, not merely below all the apostles? And feeling this towards all, he was aware how great a superiority Peter must enjoy, and he reverences him more than all men, and he esteemed him according to his dignity. The whole world was looking to Paul, the care of the Churches throughout the world was hung upon his soul, every day he transacted a thousand matters, all surrounded was he with business, presidency, corrections, counsels, warnings, instructions, the management of a thousand things; and setting all this aside, he went to Jerusalem, and there was no other pretext for his journey but to see Peter, as he himself says: 'I went up to Jerusalem to visit Peter,' so greatly did he honor him and set him before all. (St. John Chrysostom, Homily on "I withstood him to the face")

Acts 1, the appointment of Matthias. On this, St. John says:

Here is forethought for providing a teacher; here was the first who ordained a teacher. He did not say, 'We are sufficient.' So far was he beyond all vain-glory, and he looked to one thing alone. And yet he had the same power to ordain as they all collectively. ... For observe, they were an hundred and twenty, and he asks for one out of the whole body with good right, as having been put in charge of them: for to him had Christ said, "And when thou art converted, strengthen thy brethren." (Homily 3 in Acts)

Acts 9:32, "Peter, as he passed through, visiting all". St. John says here:

"And it came to pass, as Peter passed throughout all quarters, he came down also to the saints which dwelt at Lydda." Like the commander of an army, he went about, inspecting the ranks, what part was compact, what in good order, what needed his presence. See how on all occasions he goes about, foremost. When an Apostle was to be chosen, he was the foremost: when the Jews were to be told, that these were "not drunken," when the lame man was to be healed, when harangues to be made, he is before the rest: when the rulers were to be spoken to, he was the man; when Ananias, he: when healings were wrought by the shadow, still it was he. And look: where there was danger, he was the man, and where good management (was needed); but where all is calm, there they act all in common, and he demands no greater honor (than the others). (Homily 21 in Acts)

it's called the faith. That is the only key to the Kingdom of God.

"Keys", in context, most likely refers to authority. Cf. Isa. 22:20-22 for a parallel. The Fathers usually interpret them either with reference to the Church's authority to forgive sins or as a general grant of authority: thus Chrysostom gives (Homily 55 in St. Matthew) the paraphrase: What dost Thou give? tell me. "The keys of the heavens, that whatsoever thou shalt bind on earth, shall be bound in Heaven, and whatsoever thou shalt loose on earth, shall be loosed in Heaven." and says that For the Father gave to Peter the revelation of the Son; but the Son gave him to sow that of the Father and that of Himself in every part of the world; and to a mortal man He entrusted the authority over all things in Heaven, giving him the keys. To understand the keys as referring to faith also makes no sense in context. St. Peter already confessed his faith in Christ. How then should it be said to him, "I shall give to thee faith"?

There is nothing that says that he was ... the first among Apostles

Surely you realize that you have at this point wholly departed from the Patristic interpretation of Scripture. There are no grounds whatsoever for denying to him the title of "first among the apostles". St. Cyprian speaks for the primitive Church when he calls the episcopal chair the "chair of Peter", senseless unless St. Peter was the chief or first of the apostles. Moreover, Cornelius was made bishop by the judgment of God and of His Christ, by the testimony of almost all the clergy, by the suffrage of the people who were then present, and by the assembly of ancient priests and good men, when no one had been made so before him, when the place of Fabian, that is, when the place of Peter and the degree of the sacerdotal throne was vacant; (Ep. 51:8) There is one God, and Christ is one, and there is one Church, and one chair founded upon the rock by the word of the Lord. Another altar cannot be constituted nor a new priesthood be made, except the one altar and the one priesthood. Whosoever gathereth elsewhere, scattereth. (Ep. 39:5) Upon one He builds His Church, and to the same He says after His resurrection, 'feed My sheep'. And though to all His Apostles He gave an equal power yet did He set up one chair, and disposed the origin and manner of unity by his authority. The other Apostles were indeed what Peter was, but the primacy is given to Peter, and the Church and the chair is shown to be one. And all are pastors, but the flock is shown to be one, which is fed by all the Apostles with one mind and heart. (On the Unity of the Church, §4).

'I went up to Jerusalem to visit Peter,' so greatly did he honor him and set him before all

This are +Chrysostom's words...the New Testament says this:

"Then after three years I went up to Jerusalem to see Peter, and abode with him fifteen days.

But other of the apostles saw I none, save James the Lord's brother." (Gal 18-19)

+Paul went to see +Peter and +James. He went specifically to speak with +Peter but there is nothing that says here because "so greatly did he honor him and set him before all." That is +Chrysostom's version...it's ain't the Gospel.

+Paul doesn't say why he went to see +Peter or why he also saw +James but not others (maybe because they were busy baptizing the world!). +Paul also doesn't say anything about what they discussed. +Paul doesn't say "I went to see Peters because he is my leader, or because he is above me."

It seems to me these gaps were slowly "filled" by various Fathers as the time went by.

That the Apostles themselves did not buy into this interpretation as they argued who is first among them.

There is one instance where the NT "ranks" Apostles: "Peter as the "first" (Mat 10:2) but that can be because he was the oldest. It says nothing about first in authority.