Nothing much happens the first 24 hours after lay. After 24 hours the blastoderm begins to enlarge. After 2 days, you've got blood vessels beginning to radiate out. After 5 days, you have a fairly large eye spot with lots of blood vessels radiating out like a map.
I prefer to not eat eggs that have been sat upon by a broody. If I miss one for a whole day, they are usually okay. Otherwise, the egg begins to either form a chick, which produces a considerable "ick" factor for me, or the egg begins to disintegrate and become liquid yuk. Since I have a number of broodies in my coop, I crack eggs in a separate bowl before using in case I've missed an egg being sat upon. I've had to toss a few (while the rest of the family wretches).
So I'd say catch it after 1 up to 2 full days of sitting at most. Toss or let her hatch after 3 or more full days of setting.
Are the eggs fertile?
If not fertile you've got a bit more time.
Agreed with Lady. A day, two at most.
Technically safety wise they're perfectly fine to eat at any stage (look up balut if you're brave) but after a day or so they start to develop.
Are you going to let this bird(duck?) hatch?I prefer not to let them sit on their eggs because then everyone starts depositing their eggs in the nest. Duck, chicken, doesn’t matter. A couple weeks ago I had a different Muscovy sitting on her eggs (well actually only one was hers). Her egg was possibly under her for two to three days but there were a few chicken eggs that were probably only a day old.