Your people will not be relying on barter, not even in the beginning, they will be using money even if very simple money.
As far as we can tell no civilization has ever relied upon barter. Barter is basically useless in large populations for day to day transactions, you quickly run into the problem of coincidence of wants, AKA I make boats and you sell food, but you don't need any more boats but I'm hungry. debt was by far the most common in human history but that is not going to work well with your population.
Don't get me wrong Barter will be used as will the much more common debt method of exchange (sometimes called gift exchange), they are still used today after all, but they can't rely on them. Both breakdown with a large and/or specialized population. Barter due to the aforementioned coincidence of wants, barter is really only used for rare trades with strangers (aka people you don't trust) when all goods are present. And debt breaks down becasue debt only works if you know everyone, if you can trust everyone to pay their debt weeks, months, or years down the line, which means everyone needs to know everyone else intimately. Which you won't with large populations humans can't keep track of even a few hundred much less a few thousand.
But you have a real problem with large populations because most of the people you will interact with are strangers (no trust), so you cant use debt, but all the goods can't be present for most day to day transactions (I can't trade you 1/8th of a plow for breakfast, and even if you do have enough food to pay for it, that amount of food will rot before I can eat it). So people come up with some easily fractured medium if exchange, some third good you can use for exchanges, once they do that that thing whatever it is is considered money.
You don't need banks just money, nobody is taking out a loan at the beginning because nobody has any idea if said loans can be paid back, this is the same reason fiat currency is unlikely everything is too new for real trust. You are more likely to start with either commodity money or representative money, probably a mix of both.
Commodity money is just something valuable you trade with, not unlike cigarettes in prison, whether or not you smoke you still made trades using cigarettes. commodity money is just something durable, portable, and hard to counterfeit people use as a medium of exchange. Cowry shells were the most common in earth's history followed by precious metals. Grain gets used often becasue it is easy to measure and basically everyone has some, livestock is common for larger transactions.
Coins were just lumps of a valuable metal, worth whatever they were worth. Stamping the coins became a way to mark their purity, which is why it was usually the government making coins, all their coins tend to be made to the same purity so their stamp marked a value by weight.
Representative money is fairly common, it is what most of the developed world used until very recently. Usually it starts as a receipts. Receipts for something that they can trade the receipts back for, grain in a public grain silo, gold in a vault, a quota worth of military rations for labor, whatever just as long as people trust these recipes to be honored. Then some one says, "well I don't need all that X I have receipts for, maybe I can trade it for something else", and they end up trading some of the receipts for something else. this one is only likely at the start if you have some kind of central food distribution or storage, but if can replace commodity money pretty quickly.
If you want banks later you can get them in several ways, historically the first banks were either governments, wealthy merchants, or goldsmiths. Bank notes are basically just written receipts for large amounts of money.
Governments could make loans and print money because the government had so much money and made such large purchases it was often easier to just get a receipt for money than carry a million gold coins around the countryside. Everyone knew the government was trustworthy enough that the government would honor its debt. Arguably the first banks were just grain silos that issued receipts or tokens. I keep saying "the government" becasue it really does not matter what form of government.
Gold merchants had huge high quality vaults to store gold, lesser merchants would store their gold in these vaults in return for a receipt and letting the smiths be able to loan out said gold. The first banks we think of as banks were often this just people who already needed really secure storage and rented out some space in said storage.
Wealthy merchants who had a lot of money would make loans (or more often trade deals) and paper receipts were used instead of hard to transport, easy to steal, huge piles of coins. These merchants were trusted simply becasue they had enough money to honor said deals many times over. Of course this can also get you loan sharks.
This series will be very helpful for you if you want to understand how to go from simple commodity money all the way to banks. (Extra history the history of paper money)