Does anyone know how I can attach a single doc to all the customer records in one go? The thought of adding a custom field however would mean having to go into each customer and update. Also, want that anytime a new customer is added, it has the same single doc attached?

Not sure exactly where you want to attach. Or what's the use of this document gonna be. But if it's a custom field, then you can store the document in the file cabinet, Set the default value of that field to that document and for existing customers do a CSV upload to set the field internal id to that media item id.

Also store the document in your file cabinet. Then make a custom document field then use a workflow to set the field with your document