Apple Mail: messy Inbox, but no time to declutter - can I just Archive everything to see Inbox Zero again?

My Apple Mail is a gigantic mess. I don’t have the time to go through all of it right now in an orderly fashion, but I can’t stand looking at the giant number of messages I currently see.

Can I select all my current emails, and archive the whole thing to some giant folder? I want to create sorting rules to keep this from happening again, but I have no time to go through my old stuff at the moment (and there are a LOT of messages).

Also, would archiving everything across all of my accounts in Apple Mail (including Exchange, Outlook, Gmail, and Office 365) create problems if, for example, I logged into Gmail.com on its own? How would these archived messages appear?