Which “Orthodox”? The East split apart into 3 different sects in the 5th Century:
The Church of the East (extending from eastern Syria all the way to China at one point)
The Oriental Orthodox Church (Egypt, Syria and Armenia)
The Eastern Orthodox Church (then the Byzantine Empire, today Eastern Europe and Russia)
If any of these have a claim based on geography, it’s the Oriental Orthodox, since they are the ones in the original Biblical lands and have the 2 primal sees of the East - Alexandria and Antioch.
Note that centuries after the initial schism, all of these churches realized it was silly not to be in communion with Rome - and all of them rejoined the Catholic Church. But as is always the case, somebody objected, with the result that these churches split again, into the “pro-reunion with Rome” crowd and the “anti-reunion with Rome” crowd. The main ones who have rejoined are:
The Chaldean Catholic Church (from the Church of the East)
The Syriac Catholic Church (from the Oriental Orthodox)
The Melkite Catholic and Byzantine Catholic Churches (from the Eastern Orthodox)
There are also the Maronites from Lebanon, who never left the Catholic Church.
I recommend Father Adrian Fortescue’s two books on this:
babel.hathitrust.org/cgi/pt?id=pst.000033928500;view=1up;seq=2
babel.hathitrust.org/cgi/pt?id=mdp.39015004728740;view=1up;seq=7