If you solely need to print the generated document and do not need to attach to record or email it, we suggest to configure document action to only download the google doc rather than also “attach file to record,” or “download” copy to your computer and make sure the box “delete google doc after merge” is not checked. Then you can open the generated google doc (either from quick google doc URL link on Salesforce record or from your Google drive), and print from there.
If you are doing some mass printing, you can save all the google docs generated into a specific google drive folder then you can mass print those google docs. You can use a Google Drive sync app to your computer to print from the folder on the computer it syncs to. Or you can check all the google docs in a folder and then mass export them to a zip file of PDFs then extract that zip file and mass print all the PDFs.