How to farm golden goose eggs:

1. Let your hesperornis harvest 5 coel, piranha, or salmon corpses using its dive attack (1)

2. Bring it on land so it can lay a normal egg (1)

3. Let your hesperornis harvest 5 coel, piranha, or salmon corpses using its dive attack (2)

4. Bring it on land so it can lay a normal egg (2)

5. Let your hesperornis harvest 5 coel, piranha, or salmon corpses using its dive attack (3)

6. Bring it on land so it can lay a normal egg (3)

7. Let your hesperornis harvest 5 coel, piranha, or salmon corpses using its dive attack again (4)

8. Bring it on land so it can lay a golden egg

9. Repeat the entire process for more golden eggs

Remember that this process requires no luck but purely work and perserverance