How do I place my items on the map so that players can redeem and access them at any time?

To answer you question,
You can either use the Vending Machine Device to go through 1-3 items
or you can use the item spawner device to spawn 1 item (which is what most creators use)

The chests and llamas are not a great way to give out items only if it’s a battle royale map, some survival map or if you want to only give it out once.