Box supports a client-credentials grant, but only for access to information that would be available for an anonymous user. It can be used to download openly shared content, or to get information about your application.
For machine-2-machine integrations with Box, Box recommends creating a system-account, and signing in with that account once through the user-flow. If you put the resulting Refresh token into a bootstrap location for your application (like a config file, or a database entry that's used only once) then you can bootstrap your application.