Geese older than 2 usually have their favourite female aka their wife. They younger geese usually don't properly pair up until they're a bit older. Young geese tend to mate with who ever appeals to them but not a proper wife or husband (yet).
I agree by grabbing the eggs and not allowing them to sit because trust me if one goose makes a good hatch she can have many goslings.
The younger geese you can pick a random male with a random female.
The older geese hang around with their spouses so it's easy to tell which are pairs.
Goodluck!