Moving Files to a Google Folder and Subfolder

Sure - there is an action to Create a Folder in Google Drive via Pipelines and then another action to upload a file to Drive. 

In your case - you would want to create the trigger when a new record is created to then create the Folder - at which point you then want to store the Drive ID back in Quickbase in that record. You will need this when you then upload files to make sure you upload to this particular folder without having to do additional searches. 

Then you would have Pipeline(s) to upload the file to the stored Drive Folder ID from above when a new file is attached. 

From your description it sounds a little like you might have several file attachment fields in your record - I might recommend making a 'Documents' table as a child to your main record so you can upload as many attachments as you need. This also allows you to make 1 pipeline bound to the Documents record. However if you keep with having multiple file attachments in the same record - there are a couple ways you could handle it with IF conditions in your pipeline but for simplicity I would suggest setting up a different pipeline for EACH file attachment, triggered whenever a file is uploaded to that field as the trigger.