Is there a simple way to make a one piece jewelry gift box?
If you mean out of card a cube would be the simplest solution to a one piece box, try this instructable. https://www.instructables.com/id/How-to-make-a-Hexahedron-Platonic-Solid-Cube-or-/?ALLSTEPS
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I don't know any way to make a closable box that is "one piece" without using a flexible material. I once used an origami lidded cube as a gift box. That's "one piece" of paper, including the hinged lid, with no cutting or pasting. (The one I used is a middling-complex fold; there are simpler ones.)
Or do you mean a box that has been cut out of a single piece of something? If you websearch on "bandsaw boxes" you'll find one approach to turning a single piece of wood into a small cabinet with one or more drawers; that might be what you're looking for. A similar box could be done on a jigsaw or by hand with a coping saw, though that would have to be smaller -- not necessarily a bad thing depending on what the gift is.
You may also want to look up designs for puzzle boxes, which make fun (if frustrating) gift boxes.