Consensus and agreement do not define truth. Many times in history, both were against the truth and not only in religion.
Post-modern consensus varies from "I can't know anything" to "everything is valid from a certain perspective" for mostly everything in life, and that applies for many of our contemporary Orthodox who can't bring themselves up to the fact that the Church does not believe, think or act under these standards.
There is One church. Either we are it or not. And every affirmation implies infinite exclusions. I have a keyboard in front of me now. It is a keyboard, not a cat, not butter, not a supernova. Infinite exclusions is intrisic to any affirmation. That is why so many people feel uncomfortable with straight affirmations nowadays, but avoiding exclusions is also avoiding any form of knowledge. If you don't know that the thing over which you type is a keyboard (even if electronic in a Ipad), but you are not sure if you cat is not a keyboard either, then you don't know what a keyboard is at all, not even a cat.
The sacraments exist as elements of the Church. Only in the Church. If we are the Church - as it can be proven that we are - then only in the Orthodox Church there are sacraments.
Heterodox may be saved in the future, on Last Judgment day. They surely have non-ecclesiastical grace, miracles and surely God loves them. But they are not in the Church. They have never been.
Where is the proof that the Orthodox Church is the only church established by Jesus? I think that truth exists in both the RCC and Orthodox Church.
When we talk of verifiable proof, we must put theology aside. Both theologies are internally coherent and both claim revelation and correct interpretation. Correct interpretation implies that the sources are not self-explanatory as anyone can notice both from Bible and from other traditional means such as icons, fathers' works, liturgical symbology etc etc. In fact, once one gives up an arbitrary exterior interpretation to these things, one falls into the multi-denominationalism that, if correct, would only proove that Christianity is but a fairy-tale with no link to reality.
To have verifiable proof we must establish what are we trying to prove and what kind of proof it would be.
The first issue: what are we trying to prove? I think that for this subject, we must take as a given the historicity of Jesus Christ, the trustability of the New Testament as a document, that Christ actually did resurrect in flesh and, most importantly for this subject, that He did create a community that is somehow also His body. As you can see, one cannot discuss Church without first discussing Christ. A thorough analysis would have to start with Him, but that is not the aim here, so we can skip that. If all that is true, so, what we are looking for is first and foremost a community, a social group, that shares not all, but defining traits with that community that Christ created. Some changes are expected, since His first followers numbered among hundreds, maybe thousands (St. Paul mentions over 500 eye-witnesses of the resurrection; one can only estimate how many followers there were), and we know that today the four top claimants to being that community are hundreds of millions each (Orthodox, Romans, Non-Chalcedoneans and Protestants), so traits that characterize small communities and large communities cannot justify any claim for rupture. Finally, over 2000 years of history, this community has certainly gone under some changes, so we must also establish what kinds of change are just "variations on the same theme", and which ones are actual ruptures, where a certain group acquire distinctive traits different from the original community and break away from it.
As for the second issue, what kind of proof we are looking for. Certainly not mystical or theological, for that would be using the conclusion as an assumption, besides the already mentioned issue that the acceptance of these things depend on the acceptance of which community if any or if all, constitutes the continuation without rupture of the original community. We must then resort to historical and sociological tools of analysis, avoiding reading the past from the present, but allowing the past to "judge" the present. The question is not so much how we can interpret what the Apostles did and said, but how would they interpret what we are doing and saying. Would they say "Yeps, you follow Him with us" or "No, you exorcize demons in His name but you do not follow Him with us"? One small example is the repetitive issue of who the rock of Matthew 16:18 is. Each Church says it means one thing, there are fathers who say it is the correct faith Peter had expressed, others that it was Peter himself and others that it was Jesus Himself. On what criteria a non-partisan would choose? Simply what he/she *feels* sounds more right? Would he make a research to discover that the majority of the fathers said it was the faith expressed by Peter, a minority that it was Christ and the middle group that it was Peter? Is a majority vote a good criteria for this kind of question? I think neither is a good criteria. But, if you ask the Apostles, specially the one that was addressed in the event, St. Peter himself, you see that *he* explains in his epistle that the Rock is Jesus Christ. To me, that is case closed, above even the "majority" vote of the Fathers. The person involved in the case, making reference to the words used in that event, explains that Jesus is the rock. Who else would have more authority? To just improve this line of interpretation, if we go to the OT and allow it to explain the question, we see that 'rock' is an image always used to refer to God, which just confirms Peter's own explanation.
I asked all the questions I made above and used the technique of "let them explain us" instead of "I will try to explain them" to examine them all. As one can imagine, if I were to put that in words, it would be a book, but that is not the purpose of this forum.
So, I think it can be proved beyond any reasonable doubt that the commonwealth currently known as the Orthodox Church is, without rupture or change in its defining traits, the very same community that was created by Jesus 2000 years ago in Jerusalem, while Romans, Non-Chalcedoneans and Protestants all have at some point been born of ruptures with one or more of these traits and constitute other respectable, admirable in many ways, but different communities.