Excerpt from get.new: .new is a domain extension exclusively for performing new actions online: any act that leads to creation can have a quick and memorable new shortcut associated with it. Help your customers take action faster. Less time clicking means more time creating.

It would be extremely convenient to use proton.new for creating things in Proton. Everything I can think of:
proton.new/doc - New document
proton.new/sheet - New sheet
proton.new/mail & proton.new/email - New email
proton.new/event - New calendar event
proton.new/meeting - New meeting

I think the plural forms of the words should work, too: doc & docs, event & events, etc. You could also use the subdomain for this: docs.proton.new, mail.proton.new, etc.

proton.new by itself or with an invalid path (proton.new/whatever) should lead to a dashboard where you can quickly select whether you are creating a new email, document, etc.