How could it be anything else? The only Church which has existed since Christ is the Catholic Church. If He didn't establish the Catholic Church, then he didn't establish any church, and if that were the case, that would make Him a liar:
"Blessed art thou, Simon Bar-Jona: because flesh and blood hath not revealed it to thee, but my Father who is in heaven. [18] And I say to thee: That thou art Peter; and upon this rock I will build my church, and the gates of hell shall not prevail against it."
the act of baptism itself makes one born again and formally justified on the basis of their own personal holiness, but which is not Scriptural.
Formally justified on the basis of their own personal holiness? What do you mean by that?
Baptism is no guarantee of "personal holiness".
"He that believeth and is baptized, shall be saved, but he that believeth not shall be condemned"
"If thou wilt enter into life, keep the commandments"
"For he that said, Thou shalt not commit adultery, said also, Thou shalt not kill. Now if thou do not commit adultery, but shalt kill, thou art become a transgressor of the law. [12] So speak ye, and so do, as being to be judged by the law of liberty. [13] For judgment without mercy to him that hath not done mercy. And mercy exalteth itself above judgment. [14] What shall it profit, my brethren, if a man say he hath faith, but hath not works? Shall faith be able to save him? [15] And if a brother or sister be naked, and want daily food:
[16] And one of you say to them: Go in peace, be ye warmed and filled; yet give them not those things that are necessary for the body, what shall it profit? [17] So faith also, if it have not works, is dead in itself. [18] But some man will say: Thou hast faith, and I have works: shew me thy faith without works; and I will shew thee, by works, my faith. [19] Thou believest that there is one God. Thou dost well: the devils also believe and tremble. [20] But wilt thou know, O vain man, that faith without works is dead?"
That is simply another assertion in lieu of an argument, and in which your premise does not validate your conclusion.
The Lord Jesus did indeed establish a church thru faith in the gospel, and by the same faith that one True church continues as the body of Christ, as it alone consists only of believers, and is visible in the variety we seen in the NT, and in which even the church of the Laodiceans was called a church, thus one might even call Rome a church.
For no one organized church is the one true church since it consist of both unregenerate and regenerate souls, and Rome in particular is mostly the latter (i was an active one), and is fundamentally different than the NT church, engaging in progressively deformation .
Searching the Scriptures we will not find the church with men led by apostles but are not, like those who claim to be their successors in Rome, for the true apostles were those who authority was unmistakable of God, '"in all things approving ourselves as the ministers of God,..By pureness, by knowledge, by longsuffering, by kindness, by the Holy Ghost, by love unfeigned, By the word of truth, by the power of God, by the armour of righteousness on the right hand and on the left, (2 Corinthians 6:6-7) Truly the signs of an apostle were wrought among you in all patience, in signs, and wonders, and mighty deeds. (2 Corinthians 12:12)
Yet nor do we see the NT church looking to Peter as the first of a line of exalted infallible popes in Rome reigning autocratically (unhindered power, needing no agreement from the Bishops in speaking "from the chair") over the church, nor even the necessity of promise of a perpetual assured infallible magisterium.
Instead, both writings and men of God were recognized and established as such, and Truth provided and preserved, and faith, long before a church of Rome would presume itself infallible and essential for this.
And truth was established upon Scriptural substantiation in word and in power, not the premise of the assured veracity of Rome.
And Peter was the street level leader among brethren, and one of those who were manifest pillars, exercising a general pastoral role, yet who could err in leadership, and did not deliver the final verdict in Acts 15.
Meanwhile, nowhere were perpetual apostolic successors promised, unlike under the Law, and only one is seen, even though James was martyred, (Acts 12:1,2) and only one, as this was to maintain the number of the original apostles (Acts 1:15ff; Rv. 2:14)
In addition, the NT knew nothing of all revolving around the Lord's supper as the source and summit of their faith, and in the only place that it is manifestly mentioned in the life of the church then it is the church which is the focus as the body of Christ that needed to be recognized, by showing the Lord's death toward each other in their sharing of the communal meal. (1Cor. 11:17ff)
Thus the NT church knew nothing of NT pastors being distinctively titled "priests," as they did not have any unique sacrificial function, but their main function was to "preach the Word," (2Tim. 4:2) that the flock might be "nourished up in the words of faith and of good doctrine." (1Tim. 4:6)
It also knew nothing of a separate class of believers called “saints,” ” or the mention of the postmortem location of the saints being in purgatory versus with the Lord. (Lk. 24:43; 2Cor. 5:8; Phil. 1:23; 1Thes. 4:17)
And among other aberrations, based on Scripture it also knew nothing of the practice of praying to the departed, and the hyper exaltation of and devotion to Mary above that which is written; (1Cor. 4:6)
"Blessed art thou, Simon Bar-Jona: because flesh and blood hath not revealed it to thee, but my Father who is in heaven. [18] And I say to thee: That thou art Peter; and upon this rock I will build my church, and the gates of hell shall not prevail against it."
And which does not even have close to unanimous support of the "fathers," and even Catholic scholarship evidences to the contrary of and above all, in Scripture, in contrast to Peter, that the LORD Jesus is the Rock (“petra”) or "stone" (“lithos,” and which denotes a large rock in Mk. 16:4) upon which the church is built is one of the most abundantly confirmed doctrines in the Bible (petra: Rm. 9:33; 1Cor. 10:4; 1Pet. 2:8; cf. Lk. 6:48; 1Cor. 3:11; lithos: Mat. 21:42; Mk.12:10-11; Lk. 20:17-18; Act. 4:11; Rm. 9:33; Eph. 2:20; cf. Dt. 32:4, Is. 28:16) including by Peter himself. (1Pt. 2:4-8) Rome's current catechism attempts to have Peter himself as the rock as well, but also affirms: “On the rock of this faith confessed by St Peter, Christ build his Church,” (pt. 1, sec. 2, cp. 2, para. 424) which understanding some of the ancients concur with.
Formally justified on the basis of their own personal holiness? What do you mean by that? Baptism is no guarantee of "personal holiness".
You are missing your own teaching.
Although the sinner is justified by the justice of Christ, inasmuch as the Redeemer has merited for him the grace of justification (causa meritoria), nevertheless he is formally justified and made holy by his own personal justice and holiness (causa formalis)" (effected by baptism). - Catholic Encyclopedia>Sanctifying Grace
"If thou wilt enter into life, keep the commandments"
Here you are protesting against sola fide as if that marginalized works, or left the justified as simply a white washed sinner. But instead Reformers taught that faith without works is dead, but that it is a living faith that actuallly appropriates justification, not doing the commandments as under the Law, but believing with a faith that will work to fulfil the righteousness of the Law.
Peter taught that God purified the hearts of believers by faith, before baptism, (Acts 10:43-47; 15:7-9) and as Paul taught, "But to him that worketh not, but believeth on him that justifieth the un Godly, his faith is counted for righteousness. (Romans 4:5)
But it can said that "not the hearers of the law are just before God, but the doers of the law shall be justified," (Romans 2:13) and one who truly believes is baptized shall be saved, because works testify to things which accompany salvation, confirming one has true faith.
Thus is can be said Abraham believed God and was justified, not on the basis of his works, "For if Abraham were justified by works, he hath whereof to glory; but not before God. For what saith the scripture? Abraham believed God, and it was counted unto him for righteousness." (Romans 4:2-3)
Yet is can be said that "Was not Abraham our father justified by works, when he had offered Isaac his son upon the altar?" (James 2:21) For while Abraham was already justified in Gn. 15:6 by faith, yet he is also justified in a confirmatory way in testing in cp. 22, like as a prophet is justified as being one when the prophecies come true, though God knows beforehand. .