Friend, Just to butt in here for a minute------
The Society, to my limited knowlege, does say that they are the only true organization (religion) just like the first century christians. Why, they, the 144,000, are even anointed like the first century christians, unlike us of the other sheep. And the 144,000 are the only ones on the earth that are anointed like the first century christians.
The Society also says that they teach directly the Bible truths like the first century christians. Like my post above brought out - I, like you, do not believe that the Society believes that they have a continuous thread of popes or leaders throughout the entire 2,000 years since Christ.
The Society has lead us to believe, through the pages of the Watchtower and Awake articles about the faith of small groups thoughout these 2,000 years, that there has been "a" witness for God on the earth most, if not all, of these same 2,000 years.
And since there has always been "a" witness on the earth for God, why, yes, the Society can claim, if they wanted to, that there has always been Jehovah's Witnesses on the earth for God. This has been brought out in quite a few articles over the years on these Dark Ages witnesses. Remember the Gutenburg (forgive my spelling) press articles? "I'll put a bible in every plowman's hands." BTW, that is not an word-for-word translation - but the thought is correct, as I'm sure you'll agree.
The Catholic church teaches that since Peter (Saint), there has been an apostalic succession of popes to present day. This is probably not true - if you're arguing for the true religion.
But they can claim a lot of popes throughout history.
Could it be that there has always been people, even a person, on earth somewhere that has loved God just because they loved God? And they wanted to share that love with others? No need for apostalic succession - just people?