Is there a way in sharepoint where we have users in the site creating and uploading the documents in the document library but there users do not belong to any group or do not have any permission level assigned to them
At the least users must have "read level" rights to a page that contains a custom webpart which allows them to upload a file. The webpart then takes over using a trusted account and uploads the documents to a specified document library through the specified background logic.
This way you just expose a page to the users and not the document library. If you want this over a public website(internet facing) in sharepoint, you may enable anonymous access and plan for claims. That ways none of the users needs to be in a group and they can interact with the page containing the webpart.
Go to Site Actions > Site Permissions > Add User/Group > (search for the user in the people lookup - "NT Authority Authenticated Users" )
Grant them "Add Item" level rights - (before this create a custom permission called Add Item) if you just need that all users can come and upload documents across all document libraries in the site.
This should be done at a site level.
P.S (NT Authority Authenticated Users - is a special user that includes all users in the Active Directory. You only use this user when you do not want to create any SharePoint groups or Distribution Lists)