Edit: Also the great schism doesn't happen till 1054, paradox just never bothered to merge orthodox and Catholicism in the earlier starts
The Great Schism doesn't happen before the siege of Constantinople of 1204. But it was the conclusion of a very gradual process. Its roots go very deep long before that. Some argue that the
filioque imposed by Charlemagne on Latin Credo (without the consent of the Pope in Rome) was one of the first steps of this process but, in my humble opinion, it go quite more deep than that, even before Christianity.
My opinion is that it root from the Pagan Roman conquest of the Pagan Hellenic Eastern Mediterranean world. Hellenes, never accepted anything coming from the Latin part of the Roman empire (except the figure of the emperor and legions which protected their lands against foreign threats). During the time of the Roman Empire, there was more cultural opposition between Latin and Hellenes than between Pagans and Christians. In Hellenic texts of that time, Roman are generally considered being Barbarians.
This cultural mutual incomprehension between Hellenes and Latins became a religious incomprehension between Western Christianity and Eastern Christianity which culminated and became sort of "definitive" with the sack of Constantinople by Latin crusaders (albeit the Pope condemned Latin crusaders and albeit there was attempts to end the Great Schism later than that, the most known being the Florence Council of 1439).
The date of 1054 was took by modern day historians who wanted to have a symbolical date to "mark" the division but it was a non-event for most of contemporaneous Christians.