This falls into the odd request category - at least for me. My wife just finished a 2000 piece puzzle and 3 were missing. Bugged the heck out of her.
She asked me to glowforge the 3 missing pieces. I took the challenge, after all - it gave me something to play with
This was challenging - maybe I should have done it differently (like trying to forge cut directly using outline mode), but I traced the missing pieces onto a bit of paper, scanned it, fixed it up in Gimp to create a solid filled body (learned several new tricks there), pulled that into Inkscape for a bitmap to path conversion, and then printed the result using some cardboard. They fit perfectly.
What master puzzlemaker @jbmanning5 suggests is that you scan or take a picture of the puzzle from the box and print the area about where each missing piece is, glue to the cardboard and cut with the outline to get a reasonably close replacement piece.
That’s an even better idea doing it from the box cover.
So here’s what I would do using that suggestion.
Take the picture of the box where the missing piece was.
Crop it and resize as needed
Overlay the piece you modeled in your design program to where it matches the missing piece
make an outline the same size as the image. In Illustrator, you can select the image, create clipping mask, release clipping mask to make an outline automatically. Just assign it a stroke size and unique color because this will be a separate operation later
hide the shape outline and then print the graphic. Trim it to where it’s just the image left.
upload to Glowforge
score the rectangle outline; this is your placeholder for the printed image. You can either score it and just open the lid and glue it. Or, cut the placeholder out, remove with tape, xacto knife or whatever to leave the board in the same place, and then glue it and reinsert it.
ignore the outline cut and cut your puzzle piece and voila!
With three pieces, you could just set it all up in one file on one piece of material and be good to go.
Trust me all - I did consider filling in the missing image from the puzzle cover. Several things stopped me though. The only technical one was trying to stuff that scrap of cardboard (actually more paste board as it did not have corrugations) through my printer, and then going through the fun of getting a good registration the Forge. The registration is a “solved” technical challenge - easy enough to do (like us a jig, …) but would take time.
I think if I was to do more with puzzles - I would make the “beer box puzzle” from one of my local favorites. There was a nice posting suggesting that (sorry can’t find it to link it, my google foo is low this morning)