Maybe have a look at https://yoursite/admin/site_settings/category/user_preferences?filter=notification and adjust these:
Also, maybe Optional global invite code will help you. But users still need to be able to receive verification and password reset emails, unless you use something like Google auth, maybe.
If this is for some trial/testing period and you do have Google (or similar) Authentication and the global invite thing would work for you, you could disable emails. But it wouldn’t be very nice.