Most authorities on the Tarot give as its origin either the Hebrew Qabalah or the (now lost) Egyptian Mysteries, or derive the one from the other by way of Moses.
I would like to propose an alternate hypothesis. If Bill Butler's surmization that the Tarot was created in the Renaissance for the purpose of instruction in morality, then it could only have Greek philosophy at its root, as the titles and designs of the cards will bear out. This would have been acceptable to Jews (who revere Maimonedes the Peripetetic as a "Second Moses") as well as to Christians and particularly Roman Catholics, for whom Aristotle is Official Philospher.
The case of the Small Cards is broadly obvious, for they are attributed to the Four Elements of Aristotlean metaphysics.
It is also evident, with some scrutiny, that many of the Trumps are derived from Greek philosophy. Courage, Justice, Temperence, and Fortune are all major topics of Aristotle's Ethics and Politics, and the Republic and Laws of Plato. The designs of the Trumps Justice and Temperence are especially designed to illustrate Aristotle's doctrine of the Golden Mean, of which they are the prime examples.
However, if the Jews did not invent the Tarot, they gave it the master-stroke by wedding it to the Sepher Yetzirah - which itself derives plainly from Greek physics, and can be considered a useful mnemonic system thereof. For these reasons, I find it preferable to attribute much of the symbolism of the Tarot to Renaissance Classical revivalism, than to either Hebrew or Egyptian sources.
If I were to redo the Tarot to reflect this, I would probably rename "The Fool" as "Eleutheria", i.e. Happiness, which is the Summum Bonum.
It is interesting to note also that the head of the OSOGD places the origin of the Western Esoteric Tradition with the Neoplatonist Iamblicus, a student of Porphyry, who was himself the student of Plotinus, the mystic Platonist considered, himself, the founder of the Neoplatonist school and who considered Plato to be his own master (Plotinus lived more than 400 years after Plato's death).
Plato himself was almost certainly a Pythagorean, although it is somewhat disingenuous to suggest that his doctrines were theirs, just as there is doubt as to whether Plato himself would have accepted the special doctrines of Iamblicus.
It is very possible that the more important points of Greek metaphysics have their origin in India - possibly indeed by way of Egypt. Plotinus desired to emigrate to India, where he heard that "the doctrines of Plato were already established in practice." It is easy to see how a Religious Platonist, upon hearing of reincarnation, the immortality of the soul and the caste systen, could have come to that conclusion.