If you want to keep your PDFs on Google Drive (or any other cloud-mirrored service), you would need to save them as "linked" files in Zotero. See the differences between stored and linked files, including limitations:
https://www.zotero.org/support/attaching_files#stored_files_and_linked_files

Linked file setups are simplest if all files are stored in a single folder. If you have an existing folder structure from your OS that you want to match in Zotero, and maintain moving forward, that complicates things somewhat. But people often decide that trying to maintain two hierarchies - one in Zotero and one in your OS - is mostly superfluous. They often end up just relying on Zotero for that organization (it's still easy to locate named, linked files in the single Google Drive folder if necessary). [ If you really want to import PDFs as linked files from an OS folder structure that you will maintain, to matching Zotero collections, then this plugin can do that:
https://github.com/retorquere/zotero-folder-import ]

Your existing PDFs in Google Drive can be added to Zotero most simply by drag and drop with the appropriate modifier key for linked files, into Zotero collections you have created.
https://www.zotero.org/support/attaching_files#adding_files_via_the_zotero_window
The file location stored to Zotero's database will be where the file is in Google Drive when dragged (so moving a linked file later is more difficult).

Do that drag and drop in manageable-size chunks of files. If Zotero can locate metadata for the PDF, it will create a parent item for each PDF. If not, you can create a parent item yourself.
https://www.zotero.org/support/attaching_files#child_versus_standalone_attachment_files

To get *future* PDFs that you download via the Zotero Connector saved as linked files to Google Drive (and renamed according to Zotero's scheme), use Zotmoov or Attanger. Those do have the ability to save linked PDFs to sub-folders on your PC named the same as their Zotero collection, but that adds a level of complexity probably best avoided. Partly because the Zotero collections model is more like a playlist than an OS folder ...
https://www.zotero.org/support/collections_and_tags#the_zotero_collections_model

There is no way to set up a "watch" folder, where any file you add manually to your Google Drive linked-files folder would automatically get added to Zotero. You can however designate a folder for "Attach New File" in Zotmoov, where you right-click to add the latest-dated file in that folder to Zotero (and put it in the linked files folder). Attanger has a similar option.
https://github.com/wileyyugioh/zotmoov/blob/master/docs/SETTINGS_INFO.md#search-folder-for-attaching-new-files