Is there a setting to deny folder access to all user groups?

I currently have a folder called "Company 1" that only users in the group "Company 1" have access to. I set the permissions on the folder "Company 2" to only allow users in the "Company 2" group and it correctly hides the folder from Company 1 users. Unfortunately, if I add a new folder called "Company 3", users in the group "Company 1" see that folder by default.

I would like to restrict the initial folder access to only the "Staff" group so that I can individually grant access to the correct client. Is this a setting or something that is possible without having to go through multiple steps (I'm trying to keep this as simple as possible for the end-user).

Currently, I need to create the folder, edit the folder and set the permissions on the folder to only include the user groups I want. I want to default to no access for anyone except those groups specified in the Settings screen.