After you go through the steps of creating a Package as described here- and click on Generate to generate the package link you will see "Packaging is in progress".
The banner will disappear once your Package is ready. Oh and no need to keep the modal box open you can always go through these steps to check the package status:
Go to Packages in the bar on the left.
Click on the three dots in front of the package.
Click Settings and the box will appear again and you can check there the package status.
Important: The download button in the Package link will only be enabled once the packaging is done.