Who's Lydia? What's a "coyin"?
A Brief History of Coins
Something taken for granted for the last 2500 years is the existence of coins. They have served their purpose extraordinarily well, evidenced by their longevity. It is so much easier to carry a purse of coins than it is to carry a purse of oxen! Using metals generally agreed to be valuable - copper, silver, gold, and electrum (gold/silver alloy) - civilizations began minting their own coins.
Who wins the award of "first guy to make a coin" is up in the air. If you like Herodotus, he'll tell you it was the Lydians; if you like Aristotle, he'll tell you it was the wife of King Midas from Phrygia; if you like numismatists (coin folk), they'll tell you it was probably king Pheidon of Argos. Evidently, it was a Greek who made coins first. Asia did have an independent production of coins using different methods, but it is believed they developed after Greece; ultimately, the "Western" coin (based off the Greek) triumphed over the "Eastern" coin.
Essentially, take a small piece of metal of some particular weight and smash it with a hammer and anvil until it is the size you want it to be. Ta da! Coin! Quickly after this discovery came the need to verify the gold coin you were giving me was actually all gold, because you're a scumbag and I can tell just from looking at you. Thus, those kingdoms which minted their own coins began marking coins with various images. These images became linked to certain kingdoms, like the "owls" of Athena which were printed with an owl (surprise!) from the city of Athens.
Beyond this, because counterfeits exist and you're still a scumbag, merchants would mark their own coins with smaller marks called "countermarks". Then, in trading, should the coin return to them they could immediately know the coin was authentic because it had the countermark they put there.
A Roman example (37-40 AD)
All of that's great, but what if coins haven't been invented yet? Coins come into common use ~500 BC, and they are invented ~700 BC, depending on who you ask. What if my game setting is in 1500 BC? All those great tables of treasure that list various amounts of different coins are now anachronistic at best and completely worthless at worst! Woe is me!
Enter the world before coins existed!
The problem of transporting all my oxen in my purse still exists; I do not have coins as a solution. So what do I use?
Jewelry
A Gold or Electrum Egyptian Necklace - Middle Kingdom (1981-1975 BC)
A Gold or Electrum Egyptian Pendant - Early New Kingdom (1887-1425 BC)
A Bronze Luristan (Iranian) Bracelet (1000 BC)
Bracelets, chains, necklaces, earrings, buttons, broaches, rings, nose rings, anklets, pendants; instead of carrying your wealth in a pouch, you carried it on your person. For many, you displayed it on your person as a show of wealth.
A great example of this is found in Genesis 24, where Abraham's servant is seeking a wife for his son Isaac. In v.22-31 we read,
When the camels had finished drinking, the man took a gold ring weighing a half-shekel and two bracelets for her wrists weighing ten shekels in gold, and said, “Whose daughter are you? Please tell me, is there room for us to lodge in your father’s house?” She said to him, “I am the daughter of Bethuel, the son of Milcah, whom she bore to Nahor.” Again she said to him, “We have plenty of both straw and feed, and room to lodge in.” Then the man bowed low and worshiped the Lord. He said, “Blessed be the Lord, the God of my master Abraham, who has not forsaken His lovingkindness and His truth toward my master; as for me, the Lord has guided me in the way to the house of my master’s brothers.”
Then the girl ran and told her mother’s household about these things. Now Rebekah had a brother whose name was Laban; and Laban ran outside to the man at the spring. When he saw the ring and the bracelets on his sister’s wrists, and when he heard the words of Rebekah his sister, saying, “This is what the man said to me,” he went to the man; and behold, he was standing by the camels at the spring. (NASB)
These lavish gifts are a display of Abraham's wealth. A half-shekel, or "bekah", would weigh about 1/5 of an ounce. The bracelets would weigh close to 4 ounces. To put that in 2023 terms, the nose ring is about $375 and the two bracelets are worth about $7500.
Almost $8000 lavished on Rebecca, all in the form of jewelry.
Bullion
Silver Bullion from Ebla (2000-1600 BC)
Above is what is called "bullion". Bullion came in various shapes, as seen above, and were made of precious metals. Think of bullion like carrying your own mini-mint. These larger pieces of silver would be carried with you and, as needed, you would cut pieces off in appropriate weights for whatever you were purchasing. The above hoard of silver in Ebla has been analyzed and the "scraps" were found to be in common weight-measures of the time.
Say you want to purchase my sheep. I tell you it'll cost you a pim (2/3 shekel) of silver.
I have no idea if this accurate to any time period; this is an example, bear with me.
You bring out your silver bullion and shave off of a piece. You hand it to me, I lay it in my scale. Turns out, you only gave me a bekah (1/2 shekel)! You are a scumbag! You, ashamed of your wickedness, shave off another piece. Now it weighs according to the pim, and now I give you my sheep and a long reprimand about being a dishonest cheat (my pim weight is actually a shekel in weight; I'm the cheat. Bring your own weights next time).
The main difference between coins and these options is how they are measured. Coins are measured by amount; bullion or jewelry is measured by weight. While I understand 500 coins weighs more than 100 coins, the merchant of 500 BC isn't asking for a shekel of gold but rather 10 gold coins. The merchant of 1500 BC is asking for a shekel of gold. The form it takes - ear ring, nose ring, bracelet, bullion scrap, a combination - isn't as important. It just needs to be a shekel.
Miscellaneous
While the two above options are solid options, precious metals weren't the only thing assigned value. Barter is the name of the game, so antlers, horns, shells, corals, fine clothing, axe-heads, shields, cattle, horses, camels, cereal grains, oils, honey, wine, other liquors, slaves, and so on are all valuable to the right person.
A coastal city may trade primarily through their beautiful shells; a taiga town may trade primarily through antler and fur; a desert town may trade exquisite glass pieces. While metal was universal, these other items are local and add both culture and flavor to a treasure hoard.
The Game
Of course, majority of trade among the class the adventurers come from would be the trade of food-stuffs: crops and cattle. However, if the Egyptian pharaoh tombs are anything to go by, crops and living creatures don't tend to last a few thousand years.
Thus, dungeons or tombs probably won't have these items in them.
Additionally, in traveling to and fro, most parties, like real humans, probably don't want to bring a herd of cattle or cart after cart of crops with them wherever they go. It is slow, loud, resource intensive, and makes you a massive target for bad guys.
In a pre-700 BC setting, the stock of the dungeon is local things of value (antlers, shells, wine), precious metals (jewelry, bullion), craftsman items (scales, swords, fine clothing), and magic items. You don't leave with a bag of coins; you leave with an assortment of different items of unknown value.
How much is the wine worth? You'll find out back in town.
How much does the bullion weigh? You'll have to weight to find out.
What can I get for the antler of an extinct species? Beats me; go talk to so and so.
Through stocking a dungeon with these setting accurate pieces, you can build connections organically. The local hunter's guild might recognize the antler; the local temple might recognize the wine; the friendly merchant will probably give you the honest weight of the bullion - go talk to them about it.