How can we deploy a custom Word template to all Sharepoint Team sites?

In Teams, we can create new Word docs from scratch, within the Teams app. They're based on a default template - the font is Calibri, for example. Our house font is Arial, so we either want to edit the template which is automatically available to each Teams workspace, or upload a custom template that will automatically be available whenever a new Teams Sharepoint site is created.

I've figured out how to add a custom Word template to a single Teams sharepoint site, but it's laborious, and there must be a way of doing at at the 'parent' level. 

I've posted questions and support requests in various MS Teams forums, but nobody has come up with a solution, so maybe I need to look for an answer at the Sharepoint end. Just to be clear, we only want to deploy our corporate Word template to Teams workspaces, not to the Office desktop apps.