You can get it fairly early, which you should think about doing
Pokemon has a long history of providing huge boons and bonuses if you know where to look: and the open world format of Pokemon Scarlet and Violet is no different. Here’s where to find the Amulet Coin: a really useful item that you should think about grabbing as soon as possible.
Go to area three, and fight trainer battles
You know those people in front of the Pokecenter outdoor pop-ups that continuously ask if you you’ve “been having some nice battles?!” The NPC at the Medali east waypoint (in area three west) will give you the Amulet Coin as a reward for battling five other trainers in the area, which sport level 30+ Pokemon mostly of the water, ice, and electric type.
You can find the map overview of area three in the image above, as well as the exact location of the NPC (with a red arrow). All you need to do to clear out this zone is just walk the main road to the north between the NPC and any connecting area. It’s best if you take the road on the western end of town, that leads into the icy tundra in the north.
As long as you challenge someone out in the wild that’s in area three, it’ll count. Return after five battles.
What the Amulet Coin does
A classic item of sorts, the Amulet Coin does the following: “An item held by a Pokemon. It doubles any prize money received as long as the holder joins the battle at least once.”
In other words, if you give it to your lead Pokemon you can instantly hit the requirement of “joining the battle at least once,” and reap the benefits of extra cash in trainer/gym battles. It behooves you to get this item very early and start using it against gyms at the very least; so you can buy whatever Pokeballs/items you need whenever you need them.