Marking the unit
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Inkjet coder
A small printer on the line marking each unit as it passes. It is the standard industrial answer, it is fast, and it is capital a first production run usually does not have.
Hand stamp
A date stamp and an ink pad, applied to a cleared panel. It costs almost nothing, it is slow, and it is entirely workable at the scale most people start at.
Printed lot sticker
A small label printed per batch and applied by hand. Neat, reliable, and it adds a component and a step to every unit.
Written on a cleared panel
A space in the artwork with a pen line. Honest, legible if done carefully and messy if not, and it reads as handmade, which for some brands is the point.
All four need the artwork to cooperate
A clear area, flat enough, positioned where the chosen method can reach it. Designing the label without that space is what forces an ugly retrofit.
Where to put it
The base or the lower back panel, away from the front. It has to be clearly displayed rather than prominent, so somewhere a buyer can find it without it competing with the brand.
Keep a marked unit from each run
A retained sample with its own code on it, filed with the batch record. That is what makes a code useful later rather than merely compliant now.
Decide the method before the artwork is drawn
Each of the four needs a different amount of clear space in a different place. Choosing the method afterwards means either an ugly sticker across the design or a reprint.
Build the check into packing, not into inspection
The person applying the mark is the person best placed to notice it is missing. A separate inspection step later catches it after a pallet is already wrapped.