You're using "church" in several different ways. As you said, all believers make up the body of Christ, a.k.a., the church. Splitting it up into denominations doesn't negate this fact.
Now, you wrote this: "... the schism came in 1,000AD and the orthodox left because of the problem with the Pope and the problem with the filoque. We could debate which branch remained more true to the first teachings, but we cannot deny that there was one church until that time." So, if you claim that there was one church at the time -- which I question -- and it split, then it is false to claim that one or the other was first.
They co-existed! The Orthodox have as much right to say "we were first" or "we are the oldest" as the Catholics. For that matter, Protestants, since they split from the Catholic denomination, also can trace their origins back to "day one".
The Catholic denomination's claim to be the first church makes no sense.
I guess a person either accepts history or they don't.
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You wrote that "the churches that are spoken of in Revelation are churches, buildings, where the first Christians met. They're named after the place where they were built - they were not different denominations." That is simply false. They were "assemblies" (not buildings) that met in different cities and had different ideologies. Revelation 1:4a, "From John, to the seven churches that are in the province of Asia..." -- he wasn't writing to buildings but people!
To the people of Ephesus, (actually the angel), he wrote (Revelation 2:2-4), " ‘I know your works as well as your labor and steadfast endurance, and that you cannot tolerate[
g] evil. You have even put to the test those who refer to themselves as apostles (but are not), and have discovered that they are false. I am also aware that you have persisted steadfastly, endured much for the sake of my name, and have not grown weary. But I have this against you: You have departed from your first love!"
To the people of Smyrna, (actually the angel), he wrote (Revelation 2:8-10), “This is the solemn pronouncement of the one who is the first and the last, the one who was dead, but came to life: ‘I know the distress you are suffering and your poverty (but you are rich). I also know the slander against you by those who call themselves Jews and really are not, but are a synagogue of Satan. Do not be afraid of the things you are about to suffer. The devil is about to have some of you thrown into prison so you may be tested, and you will experience suffering for ten days. Remain faithful even to the point of death, and I will give you the crown that is life itself."
... and so on to the other churches.
clearly there was not one church with one doctrine, so the claim of the Catholic denomination in Rome to be the first church (with correct doctrine) is false. All one has to do is read the epistle that Paul wrote to the church at Rome to know that they also had problems, doctrinally, behaviorally, etc.
The Catholic denomination has done a superb job of manufacturing a story about itself being the first church, with Peter as the first Pope, and a handle on the true doctrine, but it doesn't stand up to scrutiny.