I have downloaded all the packages using "Restore NuGet packages" that existed in packages.config
However, they do not appear in the References, so VS is not aware of them.
Is there a way to add them automatically to the reference list? Possibly in 1 step?

The references are tracked as part of the project files and are usually added as part of a NuGet package's initial installation. Restoring the packages will just download them.
This means it sounds like you need to reinstall those specific packages whose references are missing.
To do this, run the Update-Package command in the Package Manager Console with the -reinstall flag on it.
Update-Package <package_name> -ProjectName MyProject -reinstall
Optionally, you can add the -Version flag if you need to stick with a version that's not the latest, just make this version number match that stored in your packages.config file.
Or alternatively, to reinstall all packages for a given project:
Update-Package -Reinstall -ProjectName <project_name>
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