What is the best method to FIFO small parts?

It actually depends on what the product is, how they are initially packaged to the storage area and handling requirements.

Assuming that these are not fragile or of a food based construction.

If the parts are small and are delivered to the storage in small box like containers these can be firstly marked with part number (assuming their will have a recognition number) dated as of day of receipt, and if there is multiple boxes of the same item then these can be sequentially numbered 1 to X where X is the last box.

Those picking the stock item will need to be aware of date and sequential numbering.

Those responsible for placing the items in to storage will be responsible for "rotation", placing the new stock under or behind existing stock so that the date sequence shows oldest stock closest to the picking access. as each container is emptied the next numbered box with the same date is brought forward for use.

A similar system is used for for food where the use-by, and best before dates are the key to good FIFO display/selling