The four objects on the conjuror's table are the four suits, and their history is better documented than anything else in the tarot.
European playing cards appear suddenly in the 1370s. Before that decade there is essentially no evidence of them; after it, city after city is legislating against them, and a Swiss friar writes a treatise describing the game. Cards did not develop gradually in Europe. They arrived.
Where they arrived from is known. A near-complete deck of Mamluk cards survives in Istanbul, and its suits are cups, coins, swords and polo-sticks, in a structure of numbered cards and court cards that maps directly onto the European deck. Europe took the system, kept cups, coins and swords, and turned the polo-stick, an object with no place in European life, into a baton, a staff or a club. The suit called Wands or Batons in a tarot deck is a mistranslated polo mallet.
The tarot's contribution was not the suits. It was the addition, in fifteenth-century Italy, of a fifth suit of permanent trumps and a single excuse card, on top of a deck that already existed. That is the whole innovation, and it is a game-design innovation.
This matters because the four suits are routinely presented as an ancient European symbolic system encoding the four elements. The elemental attribution is real but late, it belongs to the occult layer of the eighteenth and nineteenth centuries, and the suits themselves are Islamic in origin and were adopted for the ordinary reason that the game came with them.