Add content type file to every new document library created in a site

I created a new template via content type that I want to be available in every document library (existing and new). For existing document libraries on the site and subsites, I can manually add the template but there are 300 subsites with 4 folders each. I'm looking for a faster way to do this. Also, I want the template added to every new folder that is created on the main site or subsites. What is the solution?