Association of the four suits with other 'fours' I think probably came first i.e., four seasons, four estates, directions, cardinal virtues, elements, temperaments.
There maybe also the influence of the literary use of a deck of cards allegorically, figuratively in poems and plays, political satire.
Sometimes a literary reference or political might attach itself to particular cards, e.g. in England the Jack of Clubs was associated with treason since at least Elizabethan times.
Add also the play between the ordinary pack of cards and such things as seasons that people made a play on (four seasons, 13 weeks a season, days in a years etc.,) - such play was also associated at least from the 17th century with biblical associations (e.g., in the manner of the soldiers tale caught playing cards, who explains the cards in reference to religion (the trinity, 10 commandments, 12 disciples sort of thing).
I think the earliest keyword type list with Tarot pips/trumps (a limited set, not the whole deck) is a piedmont list c.1750.
The first complete list of keyword type list comes probably with Etteilla in the 1780's, and these continue today, having been incorporated by both exponents of the English and Continental esoteric schools.
Many of those given by Etteilla for the tarot latin suits he adapted from those used for the French suited pique decks - which he says he learnt c.1750's and received as traditional (or from a teacher from Piedmonte).
When reading with pips (whether french or latin suits), each individual card was not necessarily given a particular, individual meaning - rather it was good or bad according to its suit (e.g., commonly spades/swords were 'bad' - but might be good in context of a question in relation to war or military advancement), and no regard was given to its number, or if it was it might be nothing more to indicate that it was weak because it was low or stronger because it was high.
Anyways the first lists of keyword type meanings, for both normal (French suited) playing cards and latin suited (tarot) cards I think is with Etteilla. There is that Piedmonte list - but Etteilla is the one that has most influence in terms of the 'traditional' DM we come across to this day. Although Etteilla makes a lot of number symbolism this is mainly in regard to the stucture of the deck and card interactions. The keyword meanings he gives to the pip cards at least don't appear to be based on number symbolism (one can detect some in the trumps, e.g., in regards to his Trump 17 as Death). The emblem + number symbolism method came a little later.
If anyone has the credit of 'spelling it out' - then Etteilla is the guy you're looking for.