That can be accomplished exactly as you’re describing with the help of external tools, such as integrations. A number of users in this community are developers that can be hired to help you set something like that up (just tag your post with ‘work offered’).
But if you’re looking for a lightweight, Airtable-only solution, you could filter your views by that checkbox value. Meaning, the data wouldn’t transfer to another table, but you could view archived vs active data depending on how you set up your views.