The Apostles were, each and every one of them priests and bishops. The earliest fragments of the liturgy of the Mass date to approximately 120 AD, when disciples of the Apostles were still in leadership such as St. Ignatius of Antioch. Those fragments are probably older than the earliest existing copies of the books of the New Testament.
It would be more historically accurate to say that the early Christian (i.e Catholic) Church existed without copies or even originals of substantial portions of the New Testament since those portions had yet to be written than to suggest or claim or declaim that it existed without priests.
For example, it is manifestly obvious that the early Christian Church and some of its activities are described in the Acts of the Apostles as history and not as prophecy. Obviously, St. Paul was writing after the facts described. St. Stephen was martyred by Saul and his non-Christian associates before the former Saul could write about the incident as Paul. The Apocalypse or Revelations seems to have been written very late in the first century and after the deaths of most of the twelve Apostles and many of their contemporary priests.
There is a historical continuum that ought to be observed by those who argue in good faith (small f). On a matter of such importance as the Christian Faith, people living in 100 AD had a good idea of what happened in 50 AD and passed it on orally and in writing and discussed such matters as earnestly as we do today. Substitute freely each subsequent 50 year period and cumulate because, just as we care what happened in, say, the 2nd century as to Christianity and Christians, so have our predecessors. In this sense, it is more than a little pretentious to assume that what is not in Scripture did not occur in spite of any and all non-denominational evidence. It would fall into the same category as the calculations of Bishop Usher of the soi disant and misnamed (Anglican) Church of Ireland that the world was created approximately 4,000 B.C because of his wrinkle on the ages and intersections of the lives of the old Testament patriarchs or the idea that dinosaur fossils are a cosmic joke because they could not have existed since the Scriptures fail to mention them.
The answer to your question is: Without those specific priests who are validly consecrated as bishops, there can be no Apostolic Succession. Without Apostolic Succession, there is no authority to ordain priests. Without priests, there will be none of the following sacraments: the Holy Eucharist (and the Real Presence of Jesus Christ: Body and Blood, Soul and Divinity therein), Confirmation, Penance, Holy Orders, Extreme Unction. In such an event, the gates of hell will have prevailed which is impossible because it is guaranteed in the Peter passage of Matthew that they will not and the Scriptures tell no lies.
Christ promised that the gates of hell would not prevail against His Church, not your corrupt man-made organization.
Point by point:
Without those specific priests who are validly consecrated as bishops, there can be no Apostolic Succession
Correct, there is no Apostolic Succession.
Without Apostolic Succession, there is no authority to ordain priests.
Correct there are no "ordained priests". Christ is the only "priest".
Without priests, there will be none of the following sacraments: the Holy Eucharist (and the Real Presence of Jesus Christ: Body and Blood, Soul and Divinity therein), Confirmation, Penance, Holy Orders, Extreme Unction.
Correct. Of this list, only Communion is Biblically valid. The rest are man-made. Communion required no priest and is not the "Real Presence". Few Catholics even believe that one.
Now my turn:
From Romans Chapter 1:
22 Professing themselves to be wise, they became fools,
23 And changed the glory of the uncorruptible God into an image made like to corruptible man, and to birds, and fourfooted beasts, and creeping things.
24 Wherefore God also gave them up to uncleanness through the lusts of their own hearts, to dishonour their own bodies between themselves:
25 Who changed the truth of God into a lie, and worshipped and served the creature more than the Creator, who is blessed for ever. Amen.
26 For this cause God gave them up unto vile affections: for even their women did change the natural use into that which is against nature:
27 And likewise also the men, leaving the natural use of the woman, burned in their lust one toward another; men with men working that which is unseemly, and receiving in themselves that recompense of their error which was meet.
i.e. Those bringing idolatry and statue worship into Christianity (i.e. Catholicism) will be plagued with homosexual tendencies (Have you guys detected any of this kind of behavior lately?).
And from 1 Timothy Chapter 4:
1 Now the Spirit speaketh expressly, that in the latter times some shall depart from the faith, giving heed to seducing spirits, and doctrines of devils;
2 Speaking lies in hypocrisy; having their conscience seared with a hot iron;
3 Forbidding to marry, and commanding to abstain from meats, which God hath created to be received with thanksgiving of them which believe and know the truth.
Forbidding the priests to marry and abstaining from meat on certain days. Are these two of your demonic doctrines?