They won’t start developing until the goose goes broody and sits on them. You want to find the best before that. If they go broody they stop laying so no more new eggs for a while. But more importantly you want to get the eggs before they go broody because trying to remove a goose from a nest is a lesson in asymmetrical warfare. You want to be gentle with them. They want to murder you.

Goose eggs kept at room temperature and unwashed are good for about four weeks. But the longer you wait the more thin the whites become making them harder to manage if you want a giant fried egg. But they are still fine for other applications.